7.38. Suppose X and Y have the following joint probability mass function. . 10, p(1, 2) =. 12, p(1,3) =. 16 . 08, p(2,2) =. 12, p(2, 3) =. 10 .06, p(3, 2) =.06, p(3, 3) =. 20 p(1, 1) p(2, 1) p(3, 1) a. Find E[X] and E[Y]. b. Find Var(X) and Var(Y). c. Find Cov(X,Y). d. Find the correlation between X and Y. Also find the conditional pmfs (i) Px|Y (x |y = 2), (ii) py|x (y|r = 2), and | conditional expected values (iii) Exy (2|y = 2), (iv) Ey x (y|x = 2)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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7.38. Suppose X and Y have the following joint probability mass function.
. 10, p(1, 2) =. 12, p(1,3) =. 16
. 08, p(2,2) =. 12, p(2, 3) =. 10
.06, p(3, 2) =.06, p(3, 3) =. 20
p(1, 1)
p(2, 1)
p(3, 1)
a. Find E[X] and E[Y].
b. Find Var(X) and Var(Y).
c. Find Cov(X,Y).
d. Find the correlation between X and Y.
Transcribed Image Text:7.38. Suppose X and Y have the following joint probability mass function. . 10, p(1, 2) =. 12, p(1,3) =. 16 . 08, p(2,2) =. 12, p(2, 3) =. 10 .06, p(3, 2) =.06, p(3, 3) =. 20 p(1, 1) p(2, 1) p(3, 1) a. Find E[X] and E[Y]. b. Find Var(X) and Var(Y). c. Find Cov(X,Y). d. Find the correlation between X and Y.
Also find the conditional pmfs (i) Px|Y (x |y = 2), (ii) py|x (y|r = 2), and
| conditional expected values (iii) Exy (2|y = 2), (iv) Ey x (y|x = 2)
Transcribed Image Text:Also find the conditional pmfs (i) Px|Y (x |y = 2), (ii) py|x (y|r = 2), and | conditional expected values (iii) Exy (2|y = 2), (iv) Ey x (y|x = 2)
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