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If the joint density function of X and Y is given f(x,y) = {k(x + 2y), 0 < x < 1; 1

If the joint density function of X and Y is given f(x,y) = {k(x + 2y), 0 < x < 1; 1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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If the joint density function of X and Y is given f(x, y) = }KC* (k(x+ 2y), 0 < x < 1; 1 < y < 2 0, elsewhere a. Evaluate the value k. b. Estimate P(X+Y < 2). c. Find the marginal distribution of X and the marginal distribution of Y. d. Calculate P (1<y<3/2/x=1/2). e. Calculate P (0cxc1/2/y=3/2). f. Find the expected value of X and the expected value of Y. g. Determine whether the two random variables are dependent or independent. h. Find the expected value of g(X, Y) = X/Y3 + X2Y. i. Calculate the variance of X and the variance of Y. j. Calculate the covariance of the random variables X and Y.
Transcribed Image Text:If the joint density function of X and Y is given f(x, y) = }KC* (k(x+ 2y), 0 < x < 1; 1 < y < 2 0, elsewhere a. Evaluate the value k. b. Estimate P(X+Y < 2). c. Find the marginal distribution of X and the marginal distribution of Y. d. Calculate P (1<y<3/2/x=1/2). e. Calculate P (0cxc1/2/y=3/2). f. Find the expected value of X and the expected value of Y. g. Determine whether the two random variables are dependent or independent. h. Find the expected value of g(X, Y) = X/Y3 + X2Y. i. Calculate the variance of X and the variance of Y. j. Calculate the covariance of the random variables X and Y.
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