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4. If the joint density function of X and Y is glven f(x, y) = (x+ 2y),0

4. If the joint density function of X and Y is glven f(x, y) = (x+ 2y),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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4. If the joint density function of X and Y is glven [k(x +2y), 0 <x< 1;1 < y< 2 0, elsewhere f(x, y) = a. Evaluate the value k. b. Estimate P(X+Y<2). Find the marginal distribution of X and the marginal distribution of Y. d. Calculate P (1<y<3/2/x%31/2). Calculate P (0<x<1/2/y%3D3/2). Find the expected value of X and the expected value of Y. g. Determine whether the two random variables are dependent or independent. C. e. f. h. Find the expected value of g(X, Y) = X/Y3 +X2Y. i. Calculate the variance of X and the variance of Y. Calculate the covariance of the random variables X and Y.
Transcribed Image Text:4. If the joint density function of X and Y is glven [k(x +2y), 0 <x< 1;1 < y< 2 0, elsewhere f(x, y) = a. Evaluate the value k. b. Estimate P(X+Y<2). Find the marginal distribution of X and the marginal distribution of Y. d. Calculate P (1<y<3/2/x%31/2). Calculate P (0<x<1/2/y%3D3/2). Find the expected value of X and the expected value of Y. g. Determine whether the two random variables are dependent or independent. C. e. f. h. Find the expected value of g(X, Y) = X/Y3 +X2Y. i. Calculate the variance of X and the variance of Y. Calculate the covariance of the random variables X and Y.
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