Let X and Y have a joint pdf given by f (x, y) = {3³x₁ (3x, 0, 0 ≤ y ≤x≤1 elsewhere. 1. Find the marginal pdf's of X and Y. 2. Find P(X < 3/4 | Y≤ 1/2). 3. Let T = X + Y. Find E[T].

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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Let X and Y have a joint pdf given by
f (x, y) = {³x₁,
(3x,
0,
0 ≤ y ≤x≤1
elsewhere.
1. Find the marginal pdf's of X and Y.
2. Find P(X < 3/4|Y≤ 1/2 ).
3. Let TX + Y. Find E[T].
Transcribed Image Text:Let X and Y have a joint pdf given by f (x, y) = {³x₁, (3x, 0, 0 ≤ y ≤x≤1 elsewhere. 1. Find the marginal pdf's of X and Y. 2. Find P(X < 3/4|Y≤ 1/2 ). 3. Let TX + Y. Find E[T].
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