Page 142, 2.6.1.* Let X, Y, Z have joint pdf f(x, y, z) = 2(x + y + z)/3, 0
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please only answer page 142 2.6.1 parts a and b
Transcribed Image Text:Page 142, 2.6.1.* Let X, Y, Z have joint pdf f(x, y, z) = 2(x + y + z)/3, 0<x< 1, 0<y< 1,0 <z<
1, zero elsewhere.
(a)* Compute P(0 < X < 1/3, 0<Y <1/3, 0 < Z < 1/3) and P(0 < X < 1/3) = P(0 < Y < 1/3) = P(0
< Z < 1/3).
(b)* Calculate E(XYZ + 2X2Y2Z2). (c) Determine the joint cdf of (X, Y, Z). (d)* Find the conditional
joint density function of X and Z, given Y = y, and evaluate E(X + Z ly). (e)* Determine the
conditional density function of Z, given X = x and Y = y, and compute E(Z|x, y).
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