Let X and Y be two continuous random variables with the joint density function f(x,y) = {x – 2y, 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 0, elsewhere (a) Are the random variables X and Y independent? Justify your answer. (b) Compute the numerical value of P(Y ≥ 1, X ≤ ¹).
Let X and Y be two continuous random variables with the joint density function f(x,y) = {x – 2y, 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 0, elsewhere (a) Are the random variables X and Y independent? Justify your answer. (b) Compute the numerical value of P(Y ≥ 1, X ≤ ¹).
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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Step 1:- (a)
X and Y are independent if ,
f(x,y)= f(x)*f(y)
Given that, joint pdf of x and y is,
f(x,y)= (x-2y) ; for 0<= x<=1 and 0<=y<=1
Marginal pdf of X;
f(x)= ∫y f(x,y)dy
= ∫01 (x-2y)dy
= (xy-y2)01
= (x-1)
f(x)= (x-1)
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