text stringlengths 81 47k | source stringlengths 59 147 |
|---|---|
Question: <p>I have a two part question;</p>
<p>First Part:</p>
<p>I have an urn with 20 balls, 2 of those balls are purple, and I pull out 6 balls at random. I witness 100 realizations of this process. </p>
<p>Given the observed frequency at which I drew purple balls, how do I determine if I am really pulling balls... | https://stats.stackexchange.com/questions/3650/expected-distribution-of-random-draws |
Question: <p>Given a formula to calculate instantaneous probability of an event.<br/>
<code>f(i) = 0.0222 * e ^ (-i / 11.5)</code></p>
<p>For instance 0.0222 * e ^ (-4 / 11.5) is the probability of the event occurring exactly during the fourth months given that it hasn’t happened before. Calculate the cumulative pr... | https://stats.stackexchange.com/questions/192926/find-cumulative-probability-from-given-formula |
Question: <p>How would one go about solving the following given that the function h(x) isn’t provided in the question? I’m at a loss on where to begin.</p>
<p>Suppose h(x) is such that h(x) > 0 for x = 1,2,3,...,I. Argue that <span class="math-container">$p(x) = h(x)/ \sum_{i=1}^I h(i)$</span> is a valid pmf</p>
An... | https://stats.stackexchange.com/questions/485938/assessing-the-validity-of-a-pmf |
Question: <p>In a probability distribution, is it true that $XX$ is NOT $X^2$. That is, $XX$ is a joint distribution of $X$ and $X$ and $X^2$ is a function of $X$?</p>
Answer: <p>I think it is a notation problem: what does $XX$ represent? Note $XX$ is not a widely used notation.</p>
<p>Are you trying to use $XX$ to r... | https://stats.stackexchange.com/questions/231094/joint-distributions-and-function-of-a-random-variable |
Question: <p>I have few <code>vectors</code> (of length <code>1000</code>) representing <strong>frequency of 1000 elements for different situations</strong>.</p>
<p>e.g. Vector for situation 1 is </p>
<p><code>s1=(12, 0, 3, 4, 0, ...., 10)</code></p>
<p>and is of length <code>1000</code> (as there are <strong>1000 d... | https://stats.stackexchange.com/questions/232259/how-to-find-difference-between-multiple-probability-distributions |
Question: <p>I came across the following question and am wondering if there's a simple way to cook up a distribution achieving the Chebyshev lower bound:</p>
<p>Suppose $X$ has $\mu_X = \sigma^2_X = 9$. Define the lower bound for</p>
<p>$$\mathbb{P}[3 \leq X \leq 15]$$</p>
<p>Chebyshev tells us the answer is $\frac3... | https://stats.stackexchange.com/questions/236248/is-there-a-constructive-approach-to-creating-a-distribution-achieving-the-chebys |
Question: <p>I have one question regarding the estimation of an unknown variable.</p>
<p>Is there any way of estimating the value of a variable when you know its probability distribution?
In this case I have a variable which is distributed on the interval (1, 2), with a 25% probability of 2, and uniformly distributed ... | https://stats.stackexchange.com/questions/246951/is-there-any-way-of-estimating-the-value-of-a-variable-when-you-know-its-probabi |
Question: <p>I am trying to read a paper on factor graphs and coming from a cs background I am a little lost on the following proposition.</p>
<p>Not all distributions can be factored into a product of clique potentials.</p>
<p>The example they cite is the uniform distribution over binary vectors with an even number ... | https://stats.stackexchange.com/questions/247536/factorizing-a-probability-distribution |
Question: <p>In a survey of random questions, Jane can reply with either of the two possible answers; 'Yes' or 'No'.
The theoretical probability of Jane selecting 'Yes' for any random question in the survey is (p). </p>
<p>0 < (p) < 1 and (p) is a decimal with two decimal places (i.e. (p) can be 0.00, 0.01, 0.02... | https://stats.stackexchange.com/questions/250765/finding-the-number-of-trials-required-for-a-value-to-be-within-a-certain-range-i |
Question: <p>I'd like to model the behavior of a server A, which caches results from an upstream server B. Queries sent to server A will be forwarded to server B if the former has not already seen this query for an entry. </p>
<p>Relaxations and parameters:</p>
<ul>
<li>There are <code>x</code> total entries in serve... | https://stats.stackexchange.com/questions/260692/how-to-model-cache-hits |
Question: <p><em>I tried to use the definition:</em>
$$\displaystyle φ(x) = \frac{1}{\sqrt{2\pi}}
\int_{-\infty}^x e^{-{s^2}/{2}}\,\mathrm ds$$</p>
<p><em>So, according to <a href="http://es.symbolab.com/solver/step-by-step/%5Cint%20e%5E%7B-%5Cfrac%7Bx%5E2%7D%7B2%7D%7D" rel="nofollow noreferrer">this</a> site:</em>
$$... | https://stats.stackexchange.com/questions/262191/determine-x-x%e2%88%88r-such-that-%cf%86x-0-9505 |
Question: <p>I would like to calculate some parameters relating to customer purchasing in a retail situation. </p>
<p>I have some basic information which I can use:</p>
<p>Customer visit frequency in the form of probability distribution (I can generate Excel poisson tables using average visit frequency and these work... | https://stats.stackexchange.com/questions/183714/tricky-question-re-customer-purchase-probabilities |
Question: <p>I was asked a probability question: </p>
<p>Given three numbers i.i.d as $\text{uniform}(0,2)$, what is the probability of the median greater than $1.5$?</p>
<p>My hunch is that each number has $P(X > 1.5) = (2-1.5)/(2-0) = 0.25$, the probability of $\text{median}> 1.5$ is equivalent to "at least ... | https://stats.stackexchange.com/questions/194123/probability-of-median-1-5 |
Question: <p>I'm looking for a <strong>continuous</strong> distribution which I can parameterize such that </p>
<ol>
<li>The expected value is roughly zero</li>
<li>The expected maximum given $x$ draws from that distribution is only very weakly increasing in $x$</li>
<li>$Prob(\max $ of $ x $ draws $ > 0)$ is smal... | https://stats.stackexchange.com/questions/210039/looking-for-a-distribution-with-very-specific-properties |
Question: <p>I'd like create a stochastic vector $$\mathbf{v} = (v_1, \dots, v_n)$$ of length $n$, so that its elements are assigned weights according to a given parameter ("entropy"): the weights are either uniformly distributed with $p_i = 1/n$, or there's a "bump" at a particular position and other elements decay to... | https://stats.stackexchange.com/questions/213644/how-to-properly-initialize-a-stochastic-vector |
Question: <p>Given a set of numbers 1 through N, how many times do I have to randomly pick a number before all of the numbers have been picked a roughly equivalent (within 5% of each other) amount of times, and each one has at least been picked 100 times?</p>
<p>For example:
Given numbers 1-10, how many times do I hav... | https://stats.stackexchange.com/questions/221745/how-many-random-choices-before-they-have-all-been-picked-about-the-same-of-tim |
Question: <p>I am writing a series of program utilities which heavily utilize weighted random functions, where the user defines a probability density function as a piecewise curve with a series of <code>(x, y)</code> coordinates and gets back numbers which conform to that function. What I've been doing so far to verify... | https://stats.stackexchange.com/questions/223217/how-can-i-determine-if-a-weighed-random-function-is-working-as-expected |
Question: <p>I know that the solution is a negative binomial distribution. However, I was a looking for a proof for the same along the following lines. If the number of coin tosses is fixed to be $n$, then the distribution of number of heads follows a binomial distribution, that is
\begin{equation}
P(N_h = n_h) = \frac... | https://stats.stackexchange.com/questions/136794/in-a-statitical-experiment-involving-independent-coin-tosses-what-is-the-number |
Question: <p>I'm working on a game where I'd like damage dealt to a target to be randomized, but having troubles working out how to go about it.</p>
<p><code>N</code> projectiles are fired at a target with probability, <code>p</code>, that each missile will hit the target and damage dealt is based on the number of pro... | https://stats.stackexchange.com/questions/155412/given-hit-probability-and-number-of-projectiles-randomly-determine-number-of-hi |
Question: <blockquote>
<p>Cov(x,y) if e(x) = 2.60 and e(y) = 2.35 and e(xy) = 7.06</p>
</blockquote>
<p>i'm confused because all i know is
$$cov(x,y) = \text{correlation of xy}*sqrt(x)*sqrt(y) $$</p>
Answer: | https://stats.stackexchange.com/questions/156165/how-to-work-out-covariance-using-the-expected-value-of-x-y-and-xy |
Question: <p>Suppose $(x_1, x_2, x_3)\sim N(\mu, \Sigma)$ where $\mu\in\mathbb{R}^3$ and $\Sigma$ is a $3\times 3$ covariance matrix, are the variables $A = x_1 + x_2$ and $B = x_2 + x_3$ necessarily distributed according to a multivariate normal distribution? That is, do there exist $\nu\in\mathbb{R}^2$ and a $2\times... | https://stats.stackexchange.com/questions/173440/how-to-determine-if-random-variables-are-distributed-according-to-a-multivariate |
Question: <p>Doesn't exactly half the probability fall on either side of the mean?</p>
Answer: <blockquote>
<p>Doesn't exactly half the probability fall on either side of the mean?</p>
</blockquote>
<p>No!</p>
<p>The value half the probability falls either side of (at least with continuous distributions) is called... | https://stats.stackexchange.com/questions/177178/why-doesnt-1-2-always-equal-the-value-of-xs-cdf-at-ex |
Question: <p>I read that gaussian distribution is only defined by 2 moments i.e., mean and variance and can be only defined by these moments. Do we have distributions defined by just mean? Even for that matter, are there distributions defined by first three moments or say infinite moments. Can someone throw examples fo... | https://stats.stackexchange.com/questions/484434/pdf-and-their-relation-to-moments |
Question: <p>The SAT is used as an aid in determining college admissions. This test is a multiple choice test. To discourage random guessing, points are subtracted for wrong answers. Each question has 5 possible answers, and the test taker must pick one answer or choose not to answer the question. One point is awarded ... | https://stats.stackexchange.com/questions/271458/probability-distribution-of-random-variables |
Question: <p>Suppose <span class="math-container">$x_i, i=1, ..., n$</span> are independently distributed with mean <span class="math-container">$0$</span> and variance <span class="math-container">$\sigma^2$</span>. Then <span class="math-container">$\frac{1}{\sqrt n}\sum_{i=1}^n a_ix_i$</span> converges to a normal d... | https://stats.stackexchange.com/questions/461272/central-limit-theorem-for-non-identical-distributed-random-variables |
Question: <p>So I have the equation </p>
<p>$$h(t) = 1 + vt - \frac{1}2 gt^2 \pm sin(\omega t) $$</p>
<p>to describe the motion of a flipped coin. It is just a kinematics equation with an angular component added to it, where $h$ is the height of the coin, $v$ is the upwards velocity of the coin, $\omega$ is the angul... | https://stats.stackexchange.com/questions/70670/phase-space-distribution-of-heads-and-tails-coin-toss |
Question: <p>This is a horrible question to ask. But it would be useful to know (rather than someone spouting an <em>opinion</em> that 99.999% are/are not.).</p>
<p>It has been estimated that 18.3% of women will be raped at some point in their life time (<a href="http://www.cdc.gov/ViolencePrevention/pdf/sv-datasheet-... | https://stats.stackexchange.com/questions/71641/what-distribution-would-be-expected-for-number-rapists-vs-number-of-victims |
Question: <p>I am analyzing a timing circuit I designed, and I need to calculate the probability of a certain event (bit error). For example, I have derived this equation:</p>
<p>$(1 + x) / d < 1 / M$,</p>
<p>where x is a random variable with a normal distribution, d is a random variable with uniform distribution,... | https://stats.stackexchange.com/questions/78030/calculating-the-probability-of-an-inequality-with-two-random-variables |
Question: <p>Let's say there are $N$ balls, $l$ of them have unique colours, $N-l$ of them are black.</p>
<p>$D$ people uniformly randomly sample $n$ balls without replacement. Each person's sampling is independent of the others'. So they take $n$ balls, make copies of them, and then put the originals back for the nex... | https://stats.stackexchange.com/questions/94891/expected-number-of-trials-before-k-successes-where-multiple-successes-can-occur |
Question: <p>I’m trying to find the cumulative probability of 2 independent events (at least I think its cumulative probability). </p>
<p>I will miss work on rainy days (event 1) where my car won’t start (event 2).
The probability that my car won’t start on any given day is 20%.
The probability of rain on any given d... | https://stats.stackexchange.com/questions/97539/cumulative-probability-of-2-independent-events |
Question: <p>I am in the process of describing my research design for my dissertation and ran into a roadblock. In my design, I am converting 20 y/n responses from 190 participants to two dichotomous groups: 1). Chance level and 2). Above chance level.</p>
<p>If chance level is 50% or 10 responses correct/incorrect, h... | https://stats.stackexchange.com/questions/102643/how-do-i-determine-compute-a-cutoff-for-chance-level-not-chance-level |
Question: <p>$X$ and $Y$ are real-valued random variables such that the distribution of $(X,Y)$ is absolutely continuous with density function $p$ and let $p_x$ denote the marginal density function of $X$. Suppose that there exists a point $x_0$ such that $p_x(x_0) > 0$, $p_x$ is continuous at $x_0$, and for almost ... | https://stats.stackexchange.com/questions/104351/proof-of-conditional-probability |
Question: <p>I understand probability distribution but I am having a hard time getting a grasp on probability density function, specifically difference between dexp (density of exponential distribution) and pexp (probability distribution of exponential distribution)</p>
Answer: <p>Suppose X is an exponential random va... | https://stats.stackexchange.com/questions/111970/what-is-the-difference-between-dexp-and-pexp |
Question: <p>If $X \sim N(0,1)$, then what is the joint probability distribution of $(X+1,X)$?</p>
<p>An attempt: $f(x,x+1)=f(x|x+1)f(x+1)=f(x+1)$, so $N((0,0),(0,0;0,1))$. Note sure though...</p>
Answer: <p>First, define $Y=X+1$ to make the notation easier. What you are looking for is the pdf of YX. Here it is:</p>
... | https://stats.stackexchange.com/questions/124620/joint-probability-distribution-with-a-constant |
Question: <p>This is a novice question, which I struggling to answer. I want to find P(A>B) where A and B are random variables from two different distributions. Although two distributions that I have are not classical variants (e.g. normal or binomial etc) but a sampled distribution, I cannot use analytical approach wh... | https://stats.stackexchange.com/questions/128732/comparing-values-of-random-variables-from-sampled-distributions |
Question: <p>Law of large number ensures the convergence of sample mean to population mean. But it does not tell about the rate of convergence. Now CLT tells about the rate of convergence. Then what is the necessity of Berry-Essen theorem which also gives us the rate of convergence?</p>
Answer: | https://stats.stackexchange.com/questions/134325/rate-of-convergence-of-sample-mean |
Question: <p>Assume that $X=X_1 + X_2 +...+X_n$, where $X_i \sim CN(0,\sigma^2)$ and independent. Here $CN$ means circular complex Gaussian.</p>
<p>The question is, what is the distribution for</p>
<p>$Z = \frac{\left|X\right|^2}{\left|X_1\right|^2 + \left|X_2\right|^2+...+\left|X_n\right|^2}$</p>
<p>How can we bene... | https://stats.stackexchange.com/questions/137192/distribution-of-the-ratio-of-dependent-magnitude-square-of-complex-gaussians |
Question: <p>I am investigating a link between a random walk with drift (call it Brownian process or difusion with drift) and the CUSUM statistic.<br>
The CUSUM procedure accumulates deviations from the process mean over time, thus, if a change in the mean occurs for some reason, then the CUSUM will steadely increase o... | https://stats.stackexchange.com/questions/32784/are-first-passage-times-in-a-brownian-motion-the-same-as-the-arl-in-a-cusum |
Question: <p>In my previous question titled <a href="https://math.stackexchange.com/questions/183614/conditional-combinations-of-balls-in-bowls">"Conditional combinations of balls in bowls"</a>, is there a distribution to fit $k$ when $d \gg M$? I mean, when $d$ is so large, what is the distribution of the total number... | https://stats.stackexchange.com/questions/34517/fit-a-distribution-to-a-combinatorial-problem |
Question: <p>in a one way anova F test
when F=37.45; df1=5; df2=40
what is the P value?
I tried several software, and the result is <0.0001. I know it sounds weird that I need a really small number of possibility. However, I really need it for a publication.
I greatly appreciate if anyone can help on this issue. Ple... | https://stats.stackexchange.com/questions/41476/does-any-one-know-what-is-the-p-value-when-f-37-45-df1-5-df2-40-in-a-one-way-a |
Question: <p>Are there any other distributions with similar properties to the family of <a href="http://en.wikipedia.org/wiki/Stable_distributions" rel="nofollow">stable distributions</a>? That is, $\alpha$-stable, normal tempered stable, classical tempered stable, etc. etc. where the distribution could exhibit the fol... | https://stats.stackexchange.com/questions/49413/distributions-similar-to-the-family-of-stable-distributions |
Question: <p>I need to simulate with probability distribution number of users who are listening radio during the day. Given data : max number of users is 1000, day has 24 hours (from 0 to 24), the highest number of users should be from 11 to 15. Which probability distribution will be the best and which parameters of di... | https://stats.stackexchange.com/questions/52987/probability-distribution-to-simulate-number-of-users |
Question: <p>Is it possible to numerically calculate the probability density function for a scalar-valued function where each variable is independent and has a known distribution? For example in the simple case of <span class="math-container">$z=f(x,y)$</span>:
<span class="math-container">$$
z=y*e^x
$$</span>
if <span... | https://stats.stackexchange.com/questions/546723/probability-density-function-scalar-valued-non-linear-function-of-continuous-ran |
Question: <p>I tried looking for an existing solution for the following problem:</p>
<ul>
<li>Assume that S is a set of d elements, and R is a total order relation on S. Assume that n elements are randomly extracted from S, and then they are ordered according to R. Which is the probability that in the i-th position of ... | https://stats.stackexchange.com/questions/548420/probability-distributions-in-an-ordered-set-of-random-extracted-elements |
Question: <p>Problem:
Every roll has 4 outcomes: 1, 2, 3 and 4
There are 50% chance for 1-3 at every roll. (And that means 50% for 4)
If one roll did not give 1-3 at one roll, then it is 100% chance at the roll after. (So every second roll is guaranteed to be either 1, 2 or 3)
If rolled 1, 2 or 3 then there is equal ch... | https://stats.stackexchange.com/questions/550125/when-do-i-have-80-chance-of-6-rolls-of-either-1-2-or-3 |
Question: <p>I have read some papers about Weighted Distribution. Suppose <span class="math-container">$X$</span> is a non-negative continuous random variable with pdf <span class="math-container">$f(x)$</span>. The pdf of the weighted random variable <span class="math-container">$X_w$</span> is given by:</p>
<p><span ... | https://stats.stackexchange.com/questions/550520/why-do-we-need-weighted-distributions |
Question: <p>I have $ B $ bins and $ G $ balls, and each of the balls has a weight. I toss the balls uniformly into the bins. I select the $ K $ bins that have the highest weights as determined by the weights of the balls that are in them, and I then record the total number of balls that appear in these $ K $ bins. </p... | https://stats.stackexchange.com/questions/289244/distribution-of-number-of-balls-in-a-subset-of-bins |
Question: <p>Consider two countries competing in a game like chess. And suppose the abilities of all individuals have distributed according to Uniform[0, 1] distribution.</p>
<p>Say country <code>A</code> has population <span class="math-container">$P$</span> and country <code>B</code> has population <span class="math-... | https://stats.stackexchange.com/questions/494227/what-is-the-probability-that-the-best-n-people-come-from-china |
Question: <p>Consider a bivariate probability distribution <span class="math-container">$G$</span> and a random vector <span class="math-container">$(X_1,X_2)$</span>. Should <span class="math-container">$G$</span> satisfy any specific <strong>support</strong> restrictions in order to be an admissible probability dis... | https://stats.stackexchange.com/questions/555657/support-of-a-probability-distribution |
Question: <p>I have two decks of card. I draw from each deck independently. I need to find a specific card from each individual deck. What is the odd that on turn <span class="math-container">$n$</span>, I have found the card in each deck (this is not an assignment)?</p>
<p>From what I understand, the probability to fi... | https://stats.stackexchange.com/questions/557482/probability-finishing-on-a-given-turn-two-independent-draw |
Question: <p>Using the product distribution. I have <span class="math-container">$Z = XY$</span> with <span class="math-container">$X,Y \sim U(-1,1)$</span> and independent. Thus
<span class="math-container">\begin{align}
f_Z(z) & = \frac{1}{4} \int_{-1}^1 I_{[-1 < \frac{z}{x} < 1]} \ \frac{dx}{|x|} \\
& ... | https://stats.stackexchange.com/questions/560253/pdf-of-the-product-of-two-independent-uniform-random-variables-x-y-sim-u-1-1 |
Question: <p>This is related a previous question I posted on the product of two independent variables <a href="https://stats.stackexchange.com/questions/560253/pdf-of-the-product-of-two-independent-uniform-random-variables-x-y-sim-u-1-1">here</a>. As an alternative method, one could note that if <span class="math-conta... | https://stats.stackexchange.com/questions/560260/are-u-v-and-uv-independent-when-u-v-are-independent-and-standard-uniform |
Question: <p>I would like simulate appearance of publications in a forum and I need know what is the probability distribution of new question being asked in a forum. In my first simulation I used to normal distribution, but I think that the best distribution can be exponential distribution.</p>
Answer: <p>The exponent... | https://stats.stackexchange.com/questions/11749/probability-distribution-of-questions-in-a-forum |
Question: <p>If $F_i = G(F_{i-1}), F_0 = x$ is a sequence of distributions that converges to a degenerate distribution as $i \to \infty$, does that imply that the variance of $F_i$ decreases with $i$? </p>
<p>Specifically, I am interested in the inverse Kumaraswamy distribution: $G(x) = (1-(1-x)^a)^b$ when $a=b$... N... | https://stats.stackexchange.com/questions/16872/if-a-sequence-of-distributions-converges-to-a-degenerate-does-that-imply-the-va |
Question: <p>While considering solving the following standard question in probability in an alternative way, I get stuck with a recurrence relation. The problem is as follows:</p>
<blockquote>
<p>A bag contains <span class="math-container">$N$</span> ropes. We pick up two randomly chosen ends and tie them together unti... | https://stats.stackexchange.com/questions/489852/a-recurrence-relation-in-an-elementary-problem-in-probability |
Question: <p>Consider <span class="math-container">$N = 2^{n}$</span> random variables <span class="math-container">$X_{1}, X_{2}, \ldots, X_{N}$</span>, such that for each <span class="math-container">$i \in [N]$</span>,</p>
<p><span class="math-container">$$X_{i} \sim \Gamma\left(\frac{1}{2}, 2^{-n+1}\right). $$</spa... | https://stats.stackexchange.com/questions/497368/joint-distribution-given-normalized-gamma-distributed-components |
Question: <p>I'm kinda new to stats and trying to find info on PDFs that depend on multiple parameters, but I keep finding info only on multi-variate distributions.</p>
<p>The point is that <strong>I have only one random variable</strong> <span class="math-container">$R$</span>, but it depends on two or more parameters... | https://stats.stackexchange.com/questions/501787/basic-question-about-pdfs-multi-parameter-pdf-not-multi-variate |
Question: <p>I want to calculate how many times I will get exactly two heads if I toss 2 not-fair coins (chances of getting a head is 0.68) for 100 times?</p>
<p>Can somebody gives me a formula that I can generalize this question? (n not-fair coins where is p the chance of head for m times)</p>
Answer: <p>This is just... | https://stats.stackexchange.com/questions/502338/how-many-times-will-get-exactly-two-heads-if-i-toss-2-not-fair-coins-chances-of |
Question: <p>Let <span class="math-container">$F_1, F_2$</span> - two continuous CDF.</p>
<p>if <span class="math-container">$F_1 = F_2\quad F_2$</span> almost surely (i.e. probability of <span class="math-container">$x$</span> where <span class="math-container">$F_1(x)\neq F_2(x)$</span> is zero with respect to probab... | https://stats.stackexchange.com/questions/506072/cumulative-distribution-function-equals-almost-surely |
Question: <p>A trader learns to predict whether the stock price will rise or fall on a particular day of trading. To do this, he calls one hundred friends and asks them to toss a coin once a day, thus receiving one hundred signs of the type "heads / tails from the n-th friend." What is the probability that wi... | https://stats.stackexchange.com/questions/508660/probability-of-trial-sequence |
Question: <p>I have a set of outcomes $\{A, 2A, B, C\}$, which on a roll appear with probabilities $\{0.10, 0.15, 0.40, 0.35\}$ respectively.</p>
<p>How many rolls do I need to get 30 $A$ elements?</p>
Answer: | https://stats.stackexchange.com/questions/269611/trials-from-a-multinomial-distribution-required-to-obtain-1-item-in-particular |
Question: <p>Is there a way to normalize the given probabilities? Let's say for example I have this probability for the following words:</p>
<pre><code> I am the best today
</code></pre>
<p>$$1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1$$</p>
<p>Given that people typed the word</p>
<pre><... | https://stats.stackexchange.com/questions/273673/adjust-probabilities-to-make-it-equal-to-1 |
Question: <p>I'm working on writing an excel program that logs a series of measurements. The measurements are then used in 6 different models, all approximating the same unknown value.</p>
<p>I'd like to take the result of these 6 models and approximate the most probable value for what the unknown is. I've used averag... | https://stats.stackexchange.com/questions/274005/probable-value-of-a |
Question: <p>Suppose $X$ and $Y$ are two arbitrary random variables, and we have the following inequality that conditional on $Y=y$,
$$\textbf{Pr}(X \ge a_0 | Y=y)\le f(y),$$
where $\textbf{Pr}(\cdot)$ denotes the probability of the event, $a_0$ is a constant, and $f(y)$ is an increasing function with respect to $y$. ... | https://stats.stackexchange.com/questions/274566/is-the-following-inequality-correct-how-to-prove-it |
Question: <p>To provide some context, the exact sentence is</p>
<blockquote>
<p>for right-skewed data of the kind we consider here the method is especially sensitive to slight deviations of the data from the power-law model around xmin because most of the data, and hence most of the dynamic range of the CDF, lie in ... | https://stats.stackexchange.com/questions/278299/what-is-meant-by-dynamic-range-when-talking-about-probability-distribution |
Question: <p>The following distribution came up in my research and I'm wondering if the general class has a name and if there are computationally efficient sampling methods for it.</p>
<p>Let $\mathcal{X} = \{0,1\}^{n}$ be the sample space; these are simply $n$ dimensional vectors with each component either $0$ or $1$... | https://stats.stackexchange.com/questions/296643/a-distribution-on-binary-vectors-defined-by-a-sum |
Question: <p>Let's say I have a set of $n$ objects, and I select an object from the set with uniform probability. I do this many times, and record how many times I select each object. These counts will tend toward a uniform distribution, but an exact uniform distribution is obviously unlikely. </p>
<p>What's the chanc... | https://stats.stackexchange.com/questions/287874/probability-of-false-negative-in-uniform-distribution-test |
Question: <p>I've experimentally achieved my goal by running many random trials, generating two points according to scaled and translated gaussian distributions and counting how many times x is less than y.</p>
<p>However this is becoming a problem from a performance point of view for my application.</p>
<p>Is there ... | https://stats.stackexchange.com/questions/297927/given-two-means-and-deviations-how-can-i-compute-the-probability-that-x-y |
Question: <p>I have a large number of number sequences of different lengths consisting of 1s and 0s indicating whether an action has occurred, like:</p>
<pre><code>0111001111101
00010001111
01111111011111
</code></pre>
<p>The digits are not independent, as they represent whether an action has been performed or not,... | https://stats.stackexchange.com/questions/300718/calculate-probability-of-number-based-on-previous-numbers-in-a-non-random-sequen |
Question: <p>I have a probably very silly question, but somehow I am lost and don't get to the solution. Either it is my mistake or there is a mistake in the paper. Hopefully you can help me out!</p>
<p>The problem is as follows: The density of random variable q that is uniformly distributed between 0 and $\bar{q}$ is... | https://stats.stackexchange.com/questions/303134/taking-expectations-over-uniformly-distributed-random-variable |
Question: <p>$X$ and $Y$ are two uniformly distributed variables in interval $(a,b)$ and $(c,d)$ respectively (a>0 and c>0). </p>
<p>What is the distribution of the variable $Z$ defined as $Z=X^3/Y$?</p>
Answer: | https://stats.stackexchange.com/questions/298607/distribution-of-x%c2%b3-y-where-x-and-y-are-uniformly-distributed |
Question: <p>If we know the distribution of $X$ is symmetric, do we know anything about the shape of the distribution of $X^n$, where $n\geq 0$ but is not necessarily an integer?</p>
<p>I'm not referring to the moments of $X$, but rather the distribution of its products (but more generally, raised to the $n$th power).... | https://stats.stackexchange.com/questions/302187/distribution-of-a-random-variable-to-the-nth-power |
Question: <p>I've got a protein I'm modeling. One thing I do with it is randomly perturb the protein for a fixed amount of time at a chosen temperature, and then minimize it so that its configuration reaches a local energy minimum. Higher temperatures can reach energy minima further and further away from the starting c... | https://stats.stackexchange.com/questions/309510/probability-distribution-for-random-walk-samples-of-voronoi-decomposition-of-hig |
Question: <p>I am new to conditional probability. I would like to do some inference. If we know p(z|x) and p(z|y), can we infer p(z|x,y)? What can we deduce if x and y are independent? Thank you very much.</p>
Answer: <p>There is not enough information in $p(z|x)$ and $p(z|x)$ to determine $p(z|x,y)$. In particular, w... | https://stats.stackexchange.com/questions/315227/independent-joint-conditional-probability |
Question: <p>Where x is non-negative continuous random variable and C is a constant.</p>
Answer: <p>Yes, because $x \leq C \Leftrightarrow \sqrt{x} \leq \sqrt{C}$ for $x, C \geq 0$. </p>
<p>This means that the set of events $\{A \in \Omega: x(A) \leq C\}$ equals the set $\{A \in \Omega: \sqrt{x(A)} \leq \sqrt{C}\}$, ... | https://stats.stackexchange.com/questions/321935/is-prx-leq-c-equal-to-pr-sqrtx-leq-sqrtc |
Question: <p>Say One has a certain number of observations from a population density $p(x)$ and based on the observations decides to utilize a density $q(x)$ to approximate the unknown population density $p(x)$.</p>
<p>Can one choose $q(x)$ in such a way to get some upper bound for the $L^2$ distance or $L^1$ distance ... | https://stats.stackexchange.com/questions/324440/on-upper-bounds-on-the-distance-between-the-population-density-and-a-chosen-dens |
Question: <p>Suppose I have $n$ fair dice with 6 faces each (numbers from $1$ to $6$). I define a random variable $X_n$ - sum of numbers on dice after the throw. Is there any probability distribution I can use to calculate exact probabilities for every value of this random variable? I'm interested in a distribution tha... | https://stats.stackexchange.com/questions/330508/probability-distribution-n-dice |
Question: <p>How would I calculate the sums of two (or more) hypergeometric distributions. If, using a standard deck of cards, I want to determine the probability of draw 2 red cards and one Black Queen. I cannot just change my "good card" size and use one formula cause that wouldn't tell me what I need.</p>
<p>So, gi... | https://stats.stackexchange.com/questions/350461/how-to-compute-hypergeometric-distribution-probabilities-for-complex-events |
Question: <p>I have a website and I want to calculate the probability of clicks on the ads.</p>
<p>Let the probability that each user clicks on a link be <code>p</code> (something like <code>1%</code>)</p>
<p>if we have totally <code>N</code> users, What is the formula that computes the probability of exactly <code>... | https://stats.stackexchange.com/questions/371379/probability-of-repeated-events |
Question: <p>I have what are probably a pretty basic stats questions. I heard that under the log normal distribution, the mean =variance. Is this true? Or is this another distribution? I am having trouble finding this information online.</p>
<p>Second, if I have the mean and sd for a log normal distribution, how to I ... | https://stats.stackexchange.com/questions/372729/probabilities-under-the-log-normal-distribution-as-well-as-mean-and-sd |
Question: <p>In a question, I have 5 systems. At a given time x, the probability that they're working is based on an exponential distribution. The combination of all systems will work if any single system is working</p>
<ul>
<li>Systems fail independently</li>
</ul>
<p>How can I determine the pdf of the system reliab... | https://stats.stackexchange.com/questions/376201/pdf-of-combined-models |
Question: <p>If I draw 3 numbers: <span class="math-container">$a$</span>, <span class="math-container">$b$</span> and <span class="math-container">$c$</span> from the exact same distribution (unknown, but the same for each of the numbers).
I want to know the probability that <span class="math-container">$a$</span> is ... | https://stats.stackexchange.com/questions/383688/when-drawing-three-number-from-the-same-distribution-what-is-the-probability-of |
Question: <p>Calculate <span class="math-container">$P(X>10)$</span> where <span class="math-container">$X$</span> have Poisson distribution <span class="math-container">$Poisson(7,2)$</span>. using <span class="math-container">$R$</span></p>
<p><b>My attempt</b>
By the theory of probability we know <span class="ma... | https://stats.stackexchange.com/questions/384461/calculate-px10-where-x-have-poisson-distribution |
Question: <p>I'm doing some textbook problems on my own and there are no steps given to the solutions to some of the problems. If anyone could help me solve the following problem, much would be appreciated.</p>
<p>"A liquid culture medium contains on the average <em>m</em> bacteria per ml. A large number of samples is... | https://stats.stackexchange.com/questions/387084/how-to-find-the-value-for-average-rate |
Question: <p>I'm not even sure I'm phrasing the question properly, please let me know if there is any standard terms around this type of problem.</p>
<p>I'm trying to find an average number of attempts it would take to find a randomly placed pixel within a fixed size element. If a wrong pixel is chosen, it is removed ... | https://stats.stackexchange.com/questions/388611/how-can-i-calculate-the-probability-of-a-increasingly-likely-positive-outcome |
Question: <p>I am studying probability theory and one of the questions that I have faced is this. The problem is that I either don't know where to go about with this question or even if I do do something about it, I have no way of knowing if I'm on the right path. Is it possible to please help explain this?</p>
<p>Q. ... | https://stats.stackexchange.com/questions/394331/probability-theory-and-distribution |
Question: <p>I am using crystal ball to fit a distribution curves. Based on the fitting, the AD score is 20, p value is 0. What does it mean? Does it mean it is suitable?</p>
<p>Appreciate any help!</p>
<p>Thanks!</p>
Answer: <p>With an exceptionally high AD score of 20, and a p value that is probably equal to 0.000... | https://stats.stackexchange.com/questions/394819/what-happens-if-my-anderson-darling-score-is-more-than-10 |
Question: <p>Let <span class="math-container">$A$</span>, <span class="math-container">$B$</span> be the two players. Each one has a coin has a probability of getting heads of <span class="math-container">$p_i$</span>. Player <span class="math-container">$A$</span> always starts first. What is the probability such that... | https://stats.stackexchange.com/questions/403974/biased-coins-probability-such-that-the-first-player-throws-heads |
Question: <p>Say we have a sample space
<span class="math-container">$$\Omega_1 = \{\text{"alpha"},\text{"beta"},\text{"gamma"},\text{"delta"}\}$$</span>
if we only care about the (binary) membership in set in each event, the event space would be the power set of <span class="math-container">$\Omega_1$</span>:
<span c... | https://stats.stackexchange.com/questions/403084/accounting-for-membership-in-set-but-also-quantity-in-event |
Question: <p>If we have two independent random variables modeled as triangular distribution centered around a mean in the interval (mean - a, mean + a). 'a' is finite value. Then discretized them at fixed sub-intervals. what will be the distribution of their max?</p>
Answer: <p>Your question can be answered by conside... | https://stats.stackexchange.com/questions/416234/how-to-obtain-the-distribution-of-random-variables |
Question: <h1>Problem</h1>
<p>Say that we can find a random vector <span class="math-container">$(Y_1, \cdots, Y_n)$</span> whose distribution is identical to the conditional distribution of <span class="math-container">$(X_1, \cdots, X_n)$</span> under <span class="math-container">$f(X_1, \cdots, X_n) \le 1$</span>, ... | https://stats.stackexchange.com/questions/407932/is-a-transformation-of-a-conditional-distribution-identical-to-the-conditional-o |
Question: <p>The wikipedia page for <a href="https://en.wikipedia.org/wiki/Total_variation#Total_variation_of_probability_measures" rel="nofollow noreferrer">Total Variation</a> says that "The total variation of any probability measure is exactly one" (and is therefore not interesting).</p>
<p>I don't get why. </p>
<... | https://stats.stackexchange.com/questions/413757/total-variation-of-a-distribution |
Question: <p>I have some distributions with the same distribution, for example, Gaussian distribution or Beta distribution. My question: is the mean of the sum of these distributions equals to the sum of the means of these distributions?</p>
Answer: <p>Yes. Mostly. By the property called linearity of expectation, the ... | https://stats.stackexchange.com/questions/420123/for-any-distributions-are-mean-of-the-sum-of-the-same-distributions-equals-the |
Question: <p>To ask what I want to, let me start with an example:</p>
<p>Let <span class="math-container">$\chi(x)$</span> and <span class="math-container">$\eta(t)$</span> be two independent random variables. Then we can define a new random variables such as
<span class="math-container">$$\epsilon_1(x,t) = \chi(x) + ... | https://stats.stackexchange.com/questions/421577/an-example-of-a-random-variable-whose-both-marginal-distributions-and-itself-has |
Question: <p>How exactly the probability distributions help a statistician/data scientist in modelling/decision making? </p>
<p>Or how using distributions a data scientist derive any inference or make decisions when modelling? </p>
<p>I understand probability distributions theoretically but not sure how its utilised ... | https://stats.stackexchange.com/questions/431238/how-probability-distributions-help-a-statistical-analyst-data-scientist |
Question: <p>I'm having some problems plotting my data, and understanding what I can do with it</p>
<p>I have a dataset that looks something like:</p>
<pre><code>| Event | Score | Prob |
+-------+-------+------+
| 1 | 5 | 30% |
| 2 | 2 | 90% |
| 3 | 1 | 20% |
| 4 | 9 | 30% |
| ..... | https://stats.stackexchange.com/questions/430480/drawing-curve-from-events-that-have-probabilities |
Question: <p>In mathematics, the <a href="https://en.wikipedia.org/wiki/Multinomial_theorem" rel="nofollow noreferrer">multinomial theorem</a> </p>
<blockquote>
<p>describes how to expand a power of a sum in terms of powers of the terms in that sum. It is the generalization of the binomial theorem from binomials to ... | https://stats.stackexchange.com/questions/431476/is-it-appropriate-use-the-binomial-theorem-to-analyze-the-problem-of-rolling-dic |
Question: <p>I was wondering if there was an analytic description of the distribution of the largest <span class="math-container">$m$</span> of <span class="math-container">$n$</span> samples of a Gaussian distribution, where <span class="math-container">$n \geq m$</span>.</p>
<p>(As an example, I generated 100 sample... | https://stats.stackexchange.com/questions/435061/distribution-of-the-top-m-of-n-samples-of-a-gaussian-distribution |
Question: <p>Suppose I generate <span class="math-container">$x_1,x_2,x_3,x_4$</span> through the following procedure:</p>
<ol>
<li>Sample <span class="math-container">$x_1,x_2,x_3 \sim \text{unif}(0, 1)$</span>, iid </li>
<li>While <span class="math-container">$x_1+x_2+x_3 > 1$</span>, resample them all</li>
<li>... | https://stats.stackexchange.com/questions/438090/distribution-of-uniform-rvs-under-sum-constraint |
Question: <p>Suppose <span class="math-container">$\pi=\frac{\theta}{1-\theta}$</span> where theta is between <span class="math-container">$[0,1]$</span>. </p>
<p>If we set a uniform prior for <span class="math-container">$\pi$</span> (<span class="math-container">$p(\pi) \propto 1$</span>), what is the induced prior ... | https://stats.stackexchange.com/questions/448872/if-odd-is-uniformly-distributed-what-is-the-distribution-of-proportion |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.