Suppose X, Y have joint density function ƒ (x, y) = { # (ªy+v²), 0≤x≤1 and 0≤ y ≤1 0, (a) Check that fis a genuine joint density function. (b) Find the marginal density functions of X and Y (c) Calculate the probability P(X

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Suppose X, Y have joint density function
ƒ (x, y) = { # (ªy+y²), 0≤x≤1 and 0 ≤ y ≤1
0,
(a) Check that fis a genuine joint density function.
(b) Find the marginal density functions of X and Y
(c) Calculate the probability P(X<Y).
(d) Calculate the expectation E [X²Y].
Transcribed Image Text:Suppose X, Y have joint density function ƒ (x, y) = { # (ªy+y²), 0≤x≤1 and 0 ≤ y ≤1 0, (a) Check that fis a genuine joint density function. (b) Find the marginal density functions of X and Y (c) Calculate the probability P(X<Y). (d) Calculate the expectation E [X²Y].
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