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1. a) b) c) Let X and Y have the joint probability density function fx, y(x, y) = Cxy², 0

1. a) b) c) Let X and Y have the joint probability density function fx, y(x, y) = Cxy², 0

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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1. a) b) c) d) f) Let X and Y have the joint probability density function fx, y(x, y) = Cxy², 0<x<y<1, What must the value of C be so that fx, y(x,y) is a valid joint p.d.f.? Find the marginal probability density function of X, fx(x). Include its support. Find the marginal probability density function of Y, fy(y). Include its support. Let a>1. Find P(Y<a X). Find P(X+Y<1). e) Are X and Y independent? If not, find Cov(X, Y). zero otherwise.
Transcribed Image Text:1. a) b) c) d) f) Let X and Y have the joint probability density function fx, y(x, y) = Cxy², 0<x<y<1, What must the value of C be so that fx, y(x,y) is a valid joint p.d.f.? Find the marginal probability density function of X, fx(x). Include its support. Find the marginal probability density function of Y, fy(y). Include its support. Let a>1. Find P(Y<a X). Find P(X+Y<1). e) Are X and Y independent? If not, find Cov(X, Y). zero otherwise.
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