Let X and Y be random variables having joint density functiona. What is the value of C?b. What is the probability that X is greater than 1⁄2 and Y is less than 3/2?c. Determine the marginal density function of X and Y.d. Find E(X), E(Y), Var(X), Var(Y), σ(x), , σ(y)e. Are X and Y independent, show your solutionf. Find the correlation between X and Y variable and interpret your findings, show yoursolution.g. Find the conditional density for X given Y=y, conditional density for Y given X=x Let X and Y be random variables having joint density function[C 2x + y)Osxs1,0sys2F(x,y) =10otherwisea. What is the value of C?b. What is the probability that X is greater than % and Y is less than 3/2?c. Determine the marginal density function of X and Y.d. Find E(X) , E(), Var(X), Var(Y), σκ), , σί)e. Are X and Y independent, show your solutionf. Find the correlation between X and Y variable and interpret your findings, show yoursolution.g. Find the conditional density for X given Y=y, conditional density for Y given X=x

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Answered: Let X and Y be random variables having…

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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Question

Let X and Y be random variables having joint density function

a. What is the value of C?
b. What is the probability that X is greater than 1⁄2 and Y is less than 3/2?
c. Determine the marginal density function of X and Y.
d. Find E(X), E(Y), Var(X), Var(Y), σ(x), , σ(y)
e. Are X and Y independent, show your solution
f. Find the correlation between X and Y variable and interpret your findings, show your
solution.
g. Find the conditional density for X given Y=y, conditional density for Y given X=x