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Q2. Joint distribution of continuous random variables Suppose two random variables X and Y have a joint pdf f(z, y) = ar*y, 0

Q2. Joint distribution of continuous random variables Suppose two random variables X and Y have a joint pdf f(z, y) = ar*y, 0

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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just last subparts 4 and 5 please thank you

Q2. Joint distribution of continuous random variables Suppose two random variables X and Y have a joint pdf f(r, y) = ar³y, 0<I< 1,0<yS1, where a is a positive constant. 1. Find the value of a. 2. Find the joint edf F(r, y) = P(X < x,Y < y), 0<I < 1,0 < y < 1. %3D 3. Find the marginal pdfs fx(r), fy(y) and the marginal cdfs Fx(r), 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(r, y) = ar³y, 0<I< 1,0<yS1, where a is a positive constant. 1. Find the value of a. 2. Find the joint edf F(r, y) = P(X < x,Y < y), 0<I < 1,0 < y < 1. %3D 3. Find the marginal pdfs fx(r), fy(y) and the marginal cdfs Fx(r), 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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