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].
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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25c429c9-7b6a-480e-9489-a3695717e47d%2Fc9cce15a-4033-4b7a-8e2b-3e5c7b556f20%2Fbmwtzab_processed.jpeg&w=3840&q=75)
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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