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Q2. Joint distribution of continuous random variables Suppose two random variables X and Y have a joint pdf f(x, y) = a.x*y, 0< x < 1,0 < y < 1, %3D where a is a positive constant. 1. Find the value of a. 2. Find the joint cdf F(x, y) = P(X < x, Y < y), 0 < x< 1,0 < y < 1. 3. Find the marginal pdfs fx(x), fy (y) and the marginal cdfs Fx (x), Fy (y). 4. Are X and Y independent? Justify your answer. 5. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y).

Q2. Joint distribution of continuous random variables Suppose two random variables X and Y have a joint pdf f(x, y) = a.x*y, 0< x < 1,0 < y < 1, %3D where a is a positive constant. 1. Find the value of a. 2. Find the joint cdf F(x, y) = P(X < x, Y < y), 0 < x< 1,0 < y < 1. 3. Find the marginal pdfs fx(x), fy (y) and the marginal cdfs Fx (x), Fy (y). 4. Are X and Y independent? Justify your answer. 5. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y).

A First Course in Probability (10th Edition)
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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Q2. Joint distribution of continuous random variables Suppose two random variables X and Y have a joint pdf f(x, y) = a.x*y, 0< x < 1,0 < y S 1, %3D where a is a positive constant. 1. Find the value of a. 2. Find the joint cdf F(x, y) = P(X <x, Y < y), 0< x< 1,0 < y < 1. 3. Find the marginal pdfs fx(x), fy (y) and the marginal cdfs Fx (x), Fy (y). 4. Are X and Y independent? Justify your answer. 5. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y).
Transcribed Image Text:Q2. Joint distribution of continuous random variables Suppose two random variables X and Y have a joint pdf f(x, y) = a.x*y, 0< x < 1,0 < y S 1, %3D where a is a positive constant. 1. Find the value of a. 2. Find the joint cdf F(x, y) = P(X <x, Y < y), 0< x< 1,0 < y < 1. 3. Find the marginal pdfs fx(x), fy (y) and the marginal cdfs Fx (x), Fy (y). 4. Are X and Y independent? Justify your answer. 5. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y).
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