p = 0.78. (a) Find P(19.9 < Y < 26.9). (b) Find E(Y |x). (c) Find Var(Y |x).

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4.5-6 a b and c only

with ux = 70, of
Find
%3D
(a) E(Y|X = 76).
(b) Var(Y | X = 76).
%3D
(c) P(Y < 86| X = 76).
4.5-5. Let X denote the height in centimeters and Y the
weight in kilograms of male college students. Assume that
X and Y have a bivariate normal distribution with param-
100, µy = 84, o
%3D
eters ux =
185, o
64, and
%3D
%3D
%3D
p%3D3/5.
(a) Determine the conditional distribution of Y, given
that X = 190.
%3D
(b) Find P(86.4 < Y < 95.36|X = 190).
4.5-6. For a freshman taking introductory statistics and
majoring in psychology, let X equal the student's ACT
mathematics score and Y the student's ACT verbal score.
Assume that X and Y have a bivariate normal distribution
with ux = 22.7, o =
17.64, µy = 22.7, o = 12.25, and
%3D
%3D
p%3D0.78.
(a) Find P(19.9 < Y < 26.9).
(b) Find E(Y |x).
(c) Find Var(Y |x).
(d) Find P(19.9 < Y < 26.9| X = 23).
(e) Find P(19.9 < Y < 26.9|X 25).
(O For x = 21, 23, and 25, draw a graph of z = h(ylx)
similar to Figure 4.5-1.
%3D
Transcribed Image Text:with ux = 70, of Find %3D (a) E(Y|X = 76). (b) Var(Y | X = 76). %3D (c) P(Y < 86| X = 76). 4.5-5. Let X denote the height in centimeters and Y the weight in kilograms of male college students. Assume that X and Y have a bivariate normal distribution with param- 100, µy = 84, o %3D eters ux = 185, o 64, and %3D %3D %3D p%3D3/5. (a) Determine the conditional distribution of Y, given that X = 190. %3D (b) Find P(86.4 < Y < 95.36|X = 190). 4.5-6. For a freshman taking introductory statistics and majoring in psychology, let X equal the student's ACT mathematics score and Y the student's ACT verbal score. Assume that X and Y have a bivariate normal distribution with ux = 22.7, o = 17.64, µy = 22.7, o = 12.25, and %3D %3D p%3D0.78. (a) Find P(19.9 < Y < 26.9). (b) Find E(Y |x). (c) Find Var(Y |x). (d) Find P(19.9 < Y < 26.9| X = 23). (e) Find P(19.9 < Y < 26.9|X 25). (O For x = 21, 23, and 25, draw a graph of z = h(ylx) similar to Figure 4.5-1. %3D
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