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(5) Consider the joint p.d.f. of continuous random variables X and Y 1, y

(5) Consider the joint p.d.f. of continuous random variables X and Y 1, 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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(5) Consider the joint p.d.f. of continuous random variables X and Y: f(x,y) = { 1, y<x<y+1 and 0 ≤ y ≤ 1, 0, otherwise. (a) Find the marginal p.d.f. of X. (b) Find the marginal p.d.f. of Y.
Transcribed Image Text:(5) Consider the joint p.d.f. of continuous random variables X and Y: f(x,y) = { 1, y<x<y+1 and 0 ≤ y ≤ 1, 0, otherwise. (a) Find the marginal p.d.f. of X. (b) Find the marginal p.d.f. of Y.
(4) The joint p.d.f of the random variables X and Y is 1 ½, x² + y² >1, f(x, y) = -{ (b) P(X² +Y² < ½). 0, otherwise. Find (a) P[(X,Y) € A], where A is the sector of the unit circle in the first quadrant bounded by y = 0 and y = x
Transcribed Image Text:(4) The joint p.d.f of the random variables X and Y is 1 ½, x² + y² >1, f(x, y) = -{ (b) P(X² +Y² < ½). 0, otherwise. Find (a) P[(X,Y) € A], where A is the sector of the unit circle in the first quadrant bounded by y = 0 and y = x
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“Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved, then please specify the question number or post only that question.”

If f(x,y) is the joint probability density function then the marginal pdf of X is defined as

gx=∫fx,ydy

And the marginal pdf of Y is defined as

hy=∫fx,ydx

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