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bivariate continuous random vector (X,Y) have the following joint probability density function: { c 0

bivariate continuous random vector (X,Y) have the following joint probability density function: { c 0

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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bivariate continuous random vector (X,Y) have the following joint probability density function: {: c 0<y<1-x² and – 1<x <1 f(x, y) 0 otherwise a. Graph the support on the two dimensional X-Y plane, and find the value of c. Hint: Integrate with respect to y first, dydx. b. Find the marginal probability density function of X, fæ(x). c. Find the marginal probability density function of Y, fy(y). d. Find the conditional probability density function of X give Y=y, fæ|y(x|y). e. Are X and Y independent? Why or why not. f. Find P(Y < X + 1). Do not work out the entire integral, just set up the double integral that needs to be solved and put in the correct limits. Hint: Sketch out the region using the support from part a.
Transcribed Image Text:bivariate continuous random vector (X,Y) have the following joint probability density function: {: c 0<y<1-x² and – 1<x <1 f(x, y) 0 otherwise a. Graph the support on the two dimensional X-Y plane, and find the value of c. Hint: Integrate with respect to y first, dydx. b. Find the marginal probability density function of X, fæ(x). c. Find the marginal probability density function of Y, fy(y). d. Find the conditional probability density function of X give Y=y, fæ|y(x|y). e. Are X and Y independent? Why or why not. f. Find P(Y < X + 1). Do not work out the entire integral, just set up the double integral that needs to be solved and put in the correct limits. Hint: Sketch out the region using the support from part a.
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