Answered: Let X and Y be two 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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Question

1. Let X and Y be two random variables with the joint probability density

f (x, y) =
{ 4/3 (1 −xy), 0 < x < 1, 0 < y < 1,
0, elsewhere.
Let Z = Y 2X and W = Y be a joint transformation of (X, Y ).
(a) Draw the graph of the support of (Z, W ), and describe it mathematically.

(a) Draw the graph of the support of (Z, W ), and describe it mathematically.

(b) Find the inverse transformation.

(d) Find the joint pdf of (Z, W ).

(e) Find the pdf of Z = Y 2X from the joint pdf of (Z, W ).

1. Let X and Y be two random variables with the joint probability density
f(x, y) = {
(1 – xy), 0 < x < 1,0 <y<1,
elsewhere.
0,
Let Z = Y²X and W = Y be a joint transformation of (X, Y).
(a) Draw the graph of the support of (Z, W), and describe it mathematically.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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