2. Suppose the joint PDF of X and Y is given by - y²), 0≤x≤ 1, 0 ≤ y ≤ 1 ƒxy(x,y) = {c(x+y³²), otherwise (a) Determine c. (b) Find the probability that 0≤X≤1/4, 0≤Y≤ 1/4. (c) Determine the marginal PDFs fx(x) and fy(y).

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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 Suppose the joint PDF of X and Y is given by

2. Suppose the joint PDF of X and Y is given by
£xy(x,y) = {c(x+y³²),
[c(x+y²),
0≤ x ≤ 1, 0 ≤ y ≤ 1
otherwise
(a) Determine c.
(b) Find the probability that 0≤X≤1/4, 0≤Y≤1/4.
(c) Determine the marginal PDFs fx(x) and fy(y).
(d) Check if X and Y are independent.
Transcribed Image Text:2. Suppose the joint PDF of X and Y is given by £xy(x,y) = {c(x+y³²), [c(x+y²), 0≤ x ≤ 1, 0 ≤ y ≤ 1 otherwise (a) Determine c. (b) Find the probability that 0≤X≤1/4, 0≤Y≤1/4. (c) Determine the marginal PDFs fx(x) and fy(y). (d) Check if X and Y are independent.
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