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(i) Continuous RVs X and Y have a joint PDF (m+n+2)! S(x, y) = (-x)"y". m!n! for 0 < y

(i) Continuous RVs X and Y have a joint PDF (m+n+2)! S(x, y) = (-x)"y". m!n! for 0 < y

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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(i) Continuous RVs X and Y have a joint PDF (m+n+2)! S(x, y) = (1-x)"y". m!n! for 0 < y<x< I, where m, n are given positive integers. Check thatf is a proper PDF (i.e. its integral cquals 1). Find the marginal distributions of X and Y. Hence calculate (ii) Let X and Y be random variables. Check that Cov (X, Y) = E[1 – X] × EY – E[(1 – X)Y. (iii) Let X, Y be as in (i). Use the form of f(x, y) to express the expectations E(1- X). EY and E[(1 – X)}] in terms of factorials. Using (ii), or otherwise, show that the covariance Cov (X, Y) equals (m+1)(n+1) (m+n+3) (m+n+4)
Transcribed Image Text:(i) Continuous RVs X and Y have a joint PDF (m+n+2)! S(x, y) = (1-x)"y". m!n! for 0 < y<x< I, where m, n are given positive integers. Check thatf is a proper PDF (i.e. its integral cquals 1). Find the marginal distributions of X and Y. Hence calculate (ii) Let X and Y be random variables. Check that Cov (X, Y) = E[1 – X] × EY – E[(1 – X)Y. (iii) Let X, Y be as in (i). Use the form of f(x, y) to express the expectations E(1- X). EY and E[(1 – X)}] in terms of factorials. Using (ii), or otherwise, show that the covariance Cov (X, Y) equals (m+1)(n+1) (m+n+3) (m+n+4)
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