3. Suppose X and Y are random variables with joint PDFfxy(x,y) = 4xyl(0.1) (x) I(0.1) (y)Let U = In X and V=VY. Find the joint PDF of U and V using the method of transformation.

Answered: 3. Suppose X and Y are random variables…

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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E(XY) – E(X)E(Y) 1. The correlation of X and Y is defined as px,y if X and Y are independent, then px,y = 0. Quickly show that o(X)o(Y) 2. Let X be a random variable with P(X = k) = | for k = -1,0, 1. Let Y = X². (a) What is the p.m.f. of Y? (b) Are X and Y independent? (c) Calculate E(XY) – E(X)E(Y). (d) True or false (for any random variables X and Y): X and Y are independent if and only if E(XY) – E(X)E(Y). 3. An exam consists of twenty multiple choice questions. Each question has five different possible answers, only one of which is correct. A person randomly guesses on each question. What is the variance of the number of questions that are correct? 4. Suppose ten people get on an elevator. There are eight buttons representing floors on this elevator. Each person presses a random button. The elevator will only stop at a floor if at least one person pressed that floor's button. What is probability the elevator stops at exactly six floors? What is the variance of the number of floors…
3.2.13 Y is a continuous random variable with { 2(1- y), 0< y < 1; fy(4) = { 0, otherwise. Derive Fy(t).
3.a. Suppose Var(X1) = 2.25, Var(X2) = 2.56, and Cov(X1, X2) = -0.25. Find the correlation p of X1 and X2. b. Suppose E(Y;) = 1
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Q. 3 Let continuous random variables X and Y be independent identically distributed random variables with the following respective pdfs: fx(x) = 2e-2x;x 2 0 and fy (y) = 2e-2y;y > 0 Define a new random variable Z = X + Y. Derive moment generating function of Z, i.e. Mz(t).
12. Let the random variable X and Y have joint pdf 4 f(x,y) = (x² + 3y²), 0

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3. Suppose X and Y are random variables with joint PDF fx. (2.9)=4ryl(0.1) (x) I(0,1) (3) Let U = In X and V=VY. Find the joint PDF of U and V using the method of transformation.