Datasets:
vnpthack
/
vnpt_data

Dataset card Data Studio Files
xet
 Community
1
text
stringlengths
0
6.73k
5.0.54 b. 00018 49. a. pyy(II1) = 2, peyQll) = 4, pel) = 4,
Px(2I2) = 1/3, pyiy(3l2) = 2/3, pry(313) = 1
7. a..030 b..120 10,30 38 beEQY =1)=22 BMI = 2) _ 8,
€. yes, posy) = px(x) + py(y) EQIY —3) —3,n0
e. VXIY = 1) = 56, VXIY = 2) = 2/9,
VXI =3)=0
--- Trang 835 ---
822 Chapter 6
Sl a2x-10 b.9 63 d..0228 d. Fy) = Ory + 43 0<4 sh 0<y<h
F(x, y) = 0,.x < 0; F(x, y) = 0, y < 0;
53. a. py) = 1.x = 0,1,2,....95 prw(la) = 1/9, y = 0, F(x, y) = 6x7 + 40x <1 y >];
L2peey Dy Fay F(x, y) = 6y+ 4x5 1,0<y <b Fa y=l,
Pxy(% y) = 190,49 =0,1,2,..59%9 Ax x>ly>l
b. EQ X =x) = 5 — x/9,x=0, 1, 2, ..., 9, a linear P(25 <X < 15,25 <¥ < 75) = 23125
function of x e FU, y)=6ry, xt ys LO<x<chO<y<l,
55. a..6x,.24r 60. 60. £20 yD 0 sot a 3
F(x, y) = 3xt — 8° + 6x7 + 3y" — 8y9 + 6)? — 1,
87. a..1410 —b. 1165 xty>Laslysl
With positive correlation, the deviations from their means F(x, y) = 0, x < 0; Fl, y) = 0, y < 0;
of X and ¥ are likely to have the same sign. F(x, y) = 3x4- 8 + 67 0S x <b y>1
5 F(x, y) = 3y*-8y' + Oy 0<y<hx>1
59a. If U=Xi +X, ful =, O<u< 1, fu) = Fay) =lx>1y>1
2u—w, 1 <u < 2, folu) = 0, elsewhere i e
b. If V=X%—-xX, fio) =2-2, O<v<1, Me a2wx b.40 e100
fu) = 0, elsewhere
93. Mw(t) = 2/[(1-10007)(2-10001)}, 1500
61. 4ys[On3)P, 0 < y3 <1
65. a. gs(y) = Sy*/10°, 25/3 b. 20/3 5:
d. 1.409 Chapter 6
67. gyaiv,(ys|4) = [2/3]|lvs —4)/6) 4 < ys < 10; 8.8 lay 2 «325° «40 4552.55
69. Lins 1), 2M + Y. 3+ V,-.omln D) pal of 20 25 12 30 09
71, COeOEYO) Powyris2o) _— [rmnriesyoi)? -
+ Tarterrr ay Taroert27a) ~ [Par art 7H) E(X) = 44.5 =p
73. a..0238 — b. $2025 bes 0 112.5 312.5 800
75. slo.) = apr O0)(FOs) Fon) Fon)" Foartons pts?) 38 20 30 12
20 < J <y < 00 2 2
E(S?) = 212.25 = oF
TT. a. f,(w2) = n(n — 1) PS (Flown + wa) — Flows)" fur (oer + wa)
be. fivs (v2) = n(n — Lw32(1 — wy), 0< we < 1 a Ha | 9 a a 3 A
79. fox) =e"? — e“*, x > 0; fx) = O.x.< 0. ptxin) | 0.0000 0.0000 0.0001 0.0008 0.0055
81. a. 3/81,250 5 6 4 8 9 1.0
b Aw in keydy = K(250— 107), << 20 0.0264 0.0881 0.2013 0.3020 0.2684 0.1074
: [yay = a(asoe~ 30e +f) dex < 30 2
ly 2 Say 1 18 2 25 3 35 4
fv) = fx) dependent =
c. 3548 25.969 e, ~32.19, —.894 P(X) | 16.24.25) 20 10.0401
Prest b. P(X < 2.5) =.85
83. 7/6 er 0 1 2 3
87. ¢. If pO) = 3, p(1) = 5, p2) = 2, then 1 is the smaller of ptr) 30 40 2 08
the tworoots, so extinction is certain in this case with j. <1.
Ifp(0) = 2,p(1) = 5,p2) = .3, then 2/3 is the smaller of a. 24
the two roots, so extinetion is not certain with yu > 1. a
x P(e) x P(x) < P(x)
89. a. P((X,Y) © A) = F(b,d) — Fb, 0) ~ F(a,d) + Fla, b) UL ARE IGE CAG SS
b. PUXY)EA) = F(10, 6) — Fl, 1) — FG,6) +F(4, 1) 0.0 0.000045 1.4 0.090079 2.8 0.052077
PUXY) © A) = F(b, d) — Fb, c-1) = F(@-l, 2) + 0.2 0.000454 1.6 0.112599 3.0 0.034718
F(a-1, b-1) 0.4 0.002270 1.8 0.125110 3.2 0,021699
c. At each (vt, y), FOr, y*) is the sum of the 0.6 0.007567 2.0 0.125110 3.4 0.012764
probabilities at points (x, y) such that x < x* and 0.8 0.018917 2.2 0.113736 3.6 0.007091
yay 1.0 0.037833 2.4 0.094780 3.8 0.003732
F(x, y) x 12 0.063055__2.6 0.072908 4.0 _ 0.001866
100 250
200 350 T
y 100 30 50
0 20 25
--- Trang 836 ---
Chapter? 823
11. a. 12,.01 75. 8340
b. 12, 005 5 Fi li
¢. With less variability, the second sample is more 77+ & P= oiv/ (ow + or)
closely concentrated near 12. b. p = 9999
13. a. No, the distribution is clearly not symmetric. 79 26. 1.64
A positively skewed distribution —perhaps Weibull, gy. tf Z, and Zy are independent standard normal
bh {osnormal, or gamma. observations, then let
a X = 5Z, + 100, ¥ = 2(.5Zi + (V3/2)Z2) + 50
¢, 00000092. No, 82 is not a reasonable value for 1. ‘ (521 + (V3/2)22) +
15. a. 8366 b. no
Chapter 7
17. 43.29
19. a, .9802, 4802 b. 32 DTG byl ls x
¢. 12.74, S, an estimator for the population standard
21. a..9839 —b. 8932 deviation
. The sample proportion of students exceeding 100 in
27. a, 87,850, 19,100,116 IQ is 30/33 ~ 91
b. In case of dependence, the mean calculation is still e. 112, 5/%
valid, but not the variance calculation. °
¢. 9973 3. a. 13481, — b. 1.3481, ¥
¢. 1.78, X + 1.2828
29. a..2871 —b. .3695 a. 67. 0846
31. .0317; Because each piece is played by the same 9 1793000 b, 1,599,730. 1.601.438
musicians, there could easily be some dependence. If ~" “" 7” pete: ee
they perform the first piece slowly, then they might 7. a. 120.6 b. 1,206,000, 10,000 8
perform the second piece slowly, too, d. 120, X
33.a.45 b.68.33 c.-1, 13.67 d. 5, 68.33, 9 a.X,2113 be Kn, 119
35. a.50, 10.308 b..0076 50d. 111.56 1. b. y/pi(l —pi)/m + pall — pa) /m
e. 131.25 ¢. In part (b) replace p; with X;/n; and replace p> with