1. Suppose that the random variables X and Y have the following joint pdf: - { }(2x + 3y) for 0≤x≤ 1, 0 ≤ y ≤ 1, otherwise. f (x, y) = { (a) Find the marginal densities, fx (x) and fy (y). (Be sure to give the support set for each random variable.) (b) Compute P(X < 0.6). (c) Compute P(Y ≥ 0.5). (d) Find E(X). (e) Find E(Y).
1. Suppose that the random variables X and Y have the following joint pdf: - { }(2x + 3y) for 0≤x≤ 1, 0 ≤ y ≤ 1, otherwise. f (x, y) = { (a) Find the marginal densities, fx (x) and fy (y). (Be sure to give the support set for each random variable.) (b) Compute P(X < 0.6). (c) Compute P(Y ≥ 0.5). (d) Find E(X). (e) Find E(Y).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:1. Suppose that the random variables X and Y have the following joint pdf:
(2x+3y)
for 0 ≤ x ≤ 1, 0 ≤ y ≤ 1,
{}
otherwise.
f (x, y) = {
(a) Find the marginal densities, fx (x) and f(y). (Be sure to give the support set for each
random variable.)
(b) Compute P(X < 0.6).
(c) Compute P(Y ≥ 0.5).
(d) Find E(X).
(e) Find E(Y).
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