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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
ea4bde4c6c6616e000f17f172028f3416daa42bb	e ≈ ∑ n = 0 n m	e ≈ ∑ n = 0 n m a x σ n n ! (d n f d x n) x = μ μ n (z) {\displaystyle e\approx \textstyle \sum _{n=0}^{n_{max}}\displaystyle {\sigma ^{n} \over n!}{\biggl (}{d^{n}f \over dx^{n}}{\biggr)}_{x=\mu }\mu _{n}(z)}, where the moments of the standard normal distribution are given by:	wikipedia
d3334c3a77091de910c6a5aab162b194fb7111d3	f (x) = ∑ n = 0 ∞	f (x) = ∑ n = 0 ∞ σ n n ! (d n f d x n) x = μ μ n (z) {\displaystyle f(x)=\textstyle \sum _{n=0}^{\infty }\displaystyle {\sigma ^{n} \over n!}{\biggl (}{d^{n}f \over dx^{n}}{\biggr)}_{x=\mu }\mu _{n}(z)}, where x ∼ n (μ, σ 2) {\displaystyle x\sim n(\mu,\sigma ^{2})} is a normal random variable, and z ∼ n (0, 1) {\displ...	wikipedia
b97bf6451230e9397fda933e665fbc7d1d6c66bd	e ≈ ∑ n = 0 n m	e ≈ ∑ n = 0 n m a x 1 n ! (d n f d x n) x = μ μ n (x) {\displaystyle e\approx \textstyle \sum _{n=0}^{n_{max}}\displaystyle {1 \over n!}{\biggl (}{d^{n}f \over dx^{n}}{\biggr)}_{x=\mu }\mu _{n}(x)}, where the taylor expansion is truncated after the n m a x {\displaystyle n_{max}} -th moment.	wikipedia
8ad629bf32188bb3781401e1d7f2563c83dbb852	e = e (∑ n = 0 ∞	e = e (∑ n = 0 ∞ 1 n ! (d n f d x n) x = μ (x − μ) n) = ∑ n = 0 ∞ 1 n ! (d n f d x n) x = μ e = ∑ n = 0 ∞ 1 n ! (d n f d x n) x = μ μ n (x) {\displaystyle e=e{\biggl (}\textstyle \sum _{n=0}^{\infty }\displaystyle {1 \over n!}{\biggl (}{d^{n}f \over dx^{n}}{\biggr)}_{x=\mu }(x-\mu)^{n}{\biggr)}=\displaystyle \sum _{n=0...	wikipedia
2002b0944a14eec302b3bfde2b8883a4e624a5d6	f (x) = ∑ n = 0 ∞	f (x) = ∑ n = 0 ∞ 1 n ! (d n f d x n) x = μ (x − μ) n {\displaystyle f(x)=\displaystyle \sum _{n=0}^{\infty }\displaystyle {\frac {1}{n!}}{\biggl (}{d^{n}f \over dx^{n}}{\biggr)}_{x=\mu }(x-\mu)^{n}}, where μ = e {\displaystyle \mu =e} is the mean value of x {\displaystyle x}.	wikipedia
e960dd2f831a6e417f35cf8739af5a687e5390cf	if the moments of a certain random variable	if the moments of a certain random variable x {\displaystyle x} are known (or can be determined by integration if the probability density function is known), then it is possible to approximate the expected value of any general non-linear function f (x) {\displaystyle f(x)} as a taylor series expansion of the moments, a...	wikipedia
e772fc302f3725daf3722c00117a4db01251bb14	if any of the random variables is replaced	if any of the random variables is replaced by a deterministic variable or by a constant value (k {\displaystyle k}), the previous properties remain valid considering that e = k {\displaystyle e=k}, v a r = 0 {\displaystyle \mathrm {var} =0} and c o v = 0 {\displaystyle \mathrm {cov} =0}.	wikipedia
e8bf9baca5d39206598bdcdbb8e26b9c8cd943ff	the covariance (c o v {\displaystyle \mathrm {cov}	the covariance (c o v {\displaystyle \mathrm {cov} }) between the random variable z {\displaystyle z} resulting from an algebraic operation and the random variable x {\displaystyle x} can be calculated using the following set of rules:	wikipedia
29aae0228d0cab5f9c6d5a94519e7ab41ca0ff3a	if any of the random variables is replaced	if any of the random variables is replaced by a deterministic variable or by a constant value (k {\displaystyle k}), the previous properties remain valid considering that p = 1 {\displaystyle p=1} and e = k {\displaystyle e=k}, v a r = 0 {\displaystyle \mathrm {var} =0} and c o v = 0 {\displaystyle \mathrm {cov} =0}. s...	wikipedia
9b4e693c29e3723ad35b60ffc2ea38721f4a2b5e	if any of the random variables is replaced	if any of the random variables is replaced by a deterministic variable or by a constant value (k {\displaystyle k}), the previous properties remain valid considering that p = 1 {\displaystyle p=1} and, therefore, e = k {\displaystyle e=k}.	wikipedia
a073a6940eeb42b66adeacca3c0497b6af30cbff	in all cases, the variable z {\displaystyle z}	in all cases, the variable z {\displaystyle z} resulting from each operation is also a random variable. all commutative and associative properties of conventional algebraic operations are also valid for random variables. if any of the random variables is replaced by a deterministic variable or by a constant value, all ...	wikipedia
361ae0cbe9d09a1f93ae8331cac8c45f1f9ce729	in principle, the elementary algebra of random variables	in principle, the elementary algebra of random variables is equivalent to that of conventional non-random (or deterministic) variables. however, the changes occurring on the probability distribution of a random variable obtained after performing algebraic operations are not straightforward. therefore, the behavior of t...	wikipedia
d41cd76155fd94e747387cb0822035c655f01b95	the algebra of random variables in statistics, provides	the algebra of random variables in statistics, provides rules for the symbolic manipulation of random variables, while avoiding delving too deeply into the mathematically sophisticated ideas of probability theory. its symbolism allows the treatment of sums, products, ratios and general functions of random variables, as...	wikipedia
b95c93ee282d675ff4568da76793f481ae02e743	in march 2019 bah was appointed to the	in march 2019 bah was appointed to the google advanced technology external advisory council, a collection of experts who will consider the artificial intelligence (ai) principles of google. google disbanded ateac on april 4 2019 following criticism by google employees about another member, kay coles james.	wikipedia
771a1d3da50d3e5da81b294585a68514bcfacb54	in 2016 bah was appointed the german chair	in 2016 bah was appointed the german chair in mathematics at the african institute for mathematical sciences (aims), which is supported by the humboldt foundation. the position was welcomed by the aims community, who believe africa needs better data science infrastructure. bah organised the software engineering for app...	wikipedia
bcfb3a6a15256a777c0f66b729b95fdf11bc14fd	in 2014 bah joined the university of texas	in 2014 bah joined the university of texas at austin, where he worked on signal processing, machine learning and sampling strategies in high-dimensional data. he developed a matrix for dimensionality reduction that uses bi- lipschitz embeddings, which can exploit data redundancy.	wikipedia
fcc2071b738adcec71e75c07a87f1a62b95995da	between 2012 and 2014 bah was a postdoctoral	between 2012 and 2014 bah was a postdoctoral researcher at the École polytechnique fédérale de lausanne, where he continued his investigations into compressed sensing. he was a member of the laboratory for information and inference systems.	wikipedia
c38ec7c6e606a0984d7e3993e62a89b140bf1f8d	bah was born in the gambia. he studied	bah was born in the gambia. he studied mathematics at the university of the gambia and graduated summa cum laude in 2004. he was awarded a master of science (msc) degree from the university of oxford, where he studied mathematical modelling as a postgraduate student of wolfson college, oxford. he joined the university ...	wikipedia
98333cfbbab18301562faa353512a31d100cb570	bubacarr bah is a gambian mathematician. he is	bubacarr bah is a gambian mathematician. he is (as at july 2024) associate professor and head of data scienceat the mrc unit based at banjul, the gambia. (note that the unit is run by the london school of hygiene & tropical medicine - but was previously managed by the medical research council (united kingdom). see covi...	wikipedia
3c79ac2115873e070f75b3a9ef726f2db5b9eebe	jamie feick is an american former professional basketball	jamie feick is an american former professional basketball player. a 6 ft 9 in (2.06 m) center from michigan state university, feick played in the nba from 1996 to 2001. he played for the charlotte hornets, san antonio spurs, milwaukee bucks and new jersey nets. he was selected by the philadelphia 76ers in the second ro...	wikipedia
91d7370b018bb4360cbc5214ec87c9c53c261239	in 2008 feick joined the walmart flw bass	in 2008 feick joined the walmart flw bass fishing tournaments tour. in 2009 and 2010 he competed in the majors division, entering seven tournaments and earning $10,500. in late 2010 he left professional fishing to take the job of head basketball coach at lexington high school in lexington, ohio, where he had attended a...	wikipedia
abc17d43e28221e72568969821c77e583dd217b3	in his nba career, feick played in 201	in his nba career, feick played in 201 games and scored a total of 911 points. in the lockout-shortened 1999 season, feick averaged 11 rebounds per game in 26 games for the new jersey nets, and on january 20, 2000 recorded 12 points and 25 rebounds in one game. his last games were in the 2000–01 season, when his career...	wikipedia
7fbdf8b34b0dc94790886e3b8bff068353177f67	jamie feick (born july 3, 1974) is an	jamie feick (born july 3, 1974) is an american former professional basketball player. a 6 ft 9 in (2.06 m) center from michigan state university, feick played in the nba from 1996 to 2001. he played for the charlotte hornets, san antonio spurs, milwaukee bucks and new jersey nets. he was selected by the philadelphia 76...	wikipedia
5433b5a25e29a109fba5e18168021f065a780013	woodgate is part of birmingham, in the county	woodgate is part of birmingham, in the county of the west midlands, england, between bartley green and harborne. it is split up into 3 parts, woodgate valley south, which is the gateway to harborne. woodgate, which is next to bartley green, and woodgate valley north, often referred as part of quinton. revised plans dis...	wikipedia
65d8ad70a0314827fcf1bbec1899a6976922a92e	revised plans disclosed by birmingham council's public works	revised plans disclosed by birmingham council's public works committee in 1968 show new housing for 20,000 people (17,000 in council-built and 3,000 in private-built homes), double the original number put forward two years earlier. the plans also show a proposed woodgate/edgbaston expressway road from the m5 junction 3...	wikipedia
d8472ca1353032cd7b13c07531875b574315ac65	woodgate is part of birmingham, in the county	woodgate is part of birmingham, in the county of the west midlands, england, between bartley green and harborne. it is split up into 3 parts, woodgate valley south (also known as south woodgate), which is the gateway to harborne. woodgate, which is next to bartley green, and woodgate valley north, often referred as par...	wikipedia
b088922dc60a374d8d953cd9a37a057ec06fd4ce	the rolls-royce r is a british aero engine	the rolls-royce r is a british aero engine that was designed and built specifically for air racing purposes by rolls-royce limited. nineteen r engines were assembled in a limited production run between 1929 and 1931. developed from the rolls-royce buzzard, it was a 37-litre capacity, supercharged v-12 capable of produc...	wikipedia
885103259821bd1bc9a8a19dd6eb3ef98cd3c183	these three engines are the only ones listed	these three engines are the only ones listed by the british aircraft preservation council/rolls-royce heritage trust. the solent sky museum's s.6a, n248, (a competing aircraft in the 1929 race as an s.6, and stand-by for the 1931 race, modified as an s.6a) does not contain an r engine.	wikipedia
91e75e89ea75caf7364b2803c69ec3ae35907668	the london science museum has an r engine	the london science museum has an r engine on display which is catalogued as a stand-alone item, inventory number 1948-310. this is r27, the second sprint engine prepared for the successful air speed record attempt, and later used in thunderbolt. the science museum also has s.6b, s1595, (winner of the 1931 race and the ...	wikipedia
8fe5b04e4e519c1b424b811c1c1699bec2ea3728	the royal air force museum london at hendon	the royal air force museum london at hendon has a rolls-royce r on display (museum number 65e1139) that came to the museum in november 1965 from raf cranwell. according to the museum's records, before that it was with george eyston as one of thunderbolt's record engines. its data plate states that it is r25 under air m...	wikipedia
58a810e960436470e3476df3a18db860e2496cce	nineteen r engines were produced at derby between	nineteen r engines were produced at derby between 1929 and 1931, all given odd serial numbers. this was a rolls-royce convention when the propeller rotated anticlockwise when viewed from the front, but an exception was made for r17, the sole clockwise-rotation r engine. there is some confusion as to whether 19 or 20 r ...	wikipedia
771e0ca62e6ae69358e4ef6c5cfb31fe6be58788	i was in the workshop stitching the old	i was in the workshop stitching the old r37 back together and had the long job of lapping in all 48 valves. it was a terrible job because the engine was two monoblocs, which meant that you couldn't just lift off the heads, you had to lift what amounted to two separate engines and even then getting the valves in was no ...	wikipedia
ed825f54cbdc59dcb59f7aa550e154da7570c11d	his relationship with malcolm campbell was strained at	his relationship with malcolm campbell was strained at times: campbell, with no engineering background, would often question villa's intimate knowledge of the r engine, but his relations with donald campbell were much better, as they were of a similar age. at lake garda in 1951 villa noted the willingness of "don" to h...	wikipedia
465b0b4f31f53a4116b6c54e4ca72912a363c6a2	villa was first employed by malcolm campbell in	villa was first employed by malcolm campbell in 1922, and continued in the service of donald campbell until 1967, when campbell was killed during a record attempt on coniston water. he was the chief caretaker of their r engines until the last r-powered record attempt in 1951, after which his responsibilities centred on...	wikipedia
709ace3e85d06e659734b304e0cb0ba46f08d749	the care and maintenance of the campbell's r	the care and maintenance of the campbell's r engines was entrusted to leo villa, a cockney born to a swiss father, who was described as "the man behind the campbells" and a central figure who "fitted the first nut to the first bolt". villa learnt his trade of "aircraft mechanic" in the royal flying corps; his first job...	wikipedia
54035351d49d1b9dd41d41d10db6c12a013efa85	r39 was again used in 1939 in blue	r39 was again used in 1939 in blue bird k4. in 1947 campbell unsuccessfully converted k4 to jet power using a de havilland goblin engine. after campbell's death from natural causes in 1948, donald campbell bought k4 for a nominal sum as well as the 1935 record car when his father's effects were auctioned. he also purch...	wikipedia
f7e81ad168a3a5505087ef118be69f3dbc0066bf	in late 1935, sir malcolm campbell decided to	in late 1935, sir malcolm campbell decided to challenge the water speed record. at that point he had two napier lions and one rolls-royce r engine, r37 at his disposal, and it was decided to install the r engine in blue bird k3. during trials on loch lomond in june 1937 the engine was "slightly damaged... because of tr...	wikipedia
1063a73f83b992cf16ba235945a5b8cad8a3f892	two r engines, r17 and r19, were built	two r engines, r17 and r19, were built for sir henry segrave 's twin-engined water speed record boat miss england ii, this craft being ready for trials on windermere by june 1930. on friday 13 june, segrave was fatally injured and a rolls-royce technical advisor, victor halliwell, was killed when miss england ii capsiz...	wikipedia
99f38138301cf74f59448ec042068e3f1e7515fb	during the mid-1930s, george eyston set many speed	during the mid-1930s, george eyston set many speed records with his speed of the wind car, powered by an unsupercharged rolls-royce kestrel. in 1937 he built a massive new car, thunderbolt, powered by two r engines to attempt the absolute land speed record. at first eyston experienced clutch failure due to the combined...	wikipedia
63d4e56aa07a83130b424ac578409f8dafcb0d33	lord wakefield arranged for a replica of the	lord wakefield arranged for a replica of the rolls-royce r to be exhibited at the 1933 motor show, held at olympia, london. a press report from the event provides an insight into the public perception of the engine:	wikipedia