9. Let X and Y have the joint density f(x, y) = cx(y-x)e-y, 0≤x≤y <∞0. (a) Find c. (b) Show that: fx|y (x | y) = 6x(y-x)y-3, fy|x (y|x) = (y - x)ex-y, (c) Deduce that E(X | Y) = Y and E(Y | X) = X + 2. 0≤x≤y, 0≤x≤ y ≤ 0.
9. Let X and Y have the joint density f(x, y) = cx(y-x)e-y, 0≤x≤y <∞0. (a) Find c. (b) Show that: fx|y (x | y) = 6x(y-x)y-3, fy|x (y|x) = (y - x)ex-y, (c) Deduce that E(X | Y) = Y and E(Y | X) = X + 2. 0≤x≤y, 0≤x≤ y ≤ 0.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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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Transcribed Image Text:9. Let X and Y have the joint density f(x, y) = cx(y-x)e-y, 0≤x≤y <∞0.
(a) Find c.
(b) Show that:
fx|y (x | y) = 6x(y-x)y-3,
fy|x (y|x) = (y - x)ex-y,
(c) Deduce that E(X | Y) = Y and E(Y | X) = X + 2.
0≤x≤y,
0≤x≤ y ≤ 0.
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