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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 4YT
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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.
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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