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2. Consider the function √x (x,y)=c(x² + y²), a joint probability density function over 0

2. Consider the function √x (x,y)=c(x² + y²), a joint probability density function over 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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The dark spaces between sentences in the picture with the question are given in the second picture. Part d is P(X>2.5 and Y
2. Consider the function Swy (x,y)= c(x² + y²), a joint probability density function over 0<x<5 and 0<y<5 a. Determine the value of c that makes the function(x) a valid pdf. b. Find the marginal pdf of X, x(x) C. Find the marginal pdf of Y, y(x) P(X> 2.5 and Y <1.5) d. e. Are X and Y independent? You must demonstrate this using the definition. f. What is the correlation between X and Y? (20 points) g. What is the probability that Y<1.5 given X=0? (10 points)
Transcribed Image Text:2. Consider the function Swy (x,y)= c(x² + y²), a joint probability density function over 0<x<5 and 0<y<5 a. Determine the value of c that makes the function(x) a valid pdf. b. Find the marginal pdf of X, x(x) C. Find the marginal pdf of Y, y(x) P(X> 2.5 and Y <1.5) d. e. Are X and Y independent? You must demonstrate this using the definition. f. What is the correlation between X and Y? (20 points) g. What is the probability that Y<1.5 given X=0? (10 points)
0<x<5 P(X> 2.5 and Y <1.5) fx (x,y)=c(x² + y²) 0<y<5 fx (x) fy (y) £xy (x, y)
Transcribed Image Text:0<x<5 P(X> 2.5 and Y <1.5) fx (x,y)=c(x² + y²) 0<y<5 fx (x) fy (y) £xy (x, y)
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