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Consider the function fy (x,y)=c(x² +y² ), a joint probability density function over 0 2.5 and Y <1.5)

Consider the function fy (x,y)=c(x² +y² ), a joint probability density function over 0 2.5 and Y <1.5)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider the function fy (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 fry (x, y) a valid pdf. b. Find the marginal pdf of X, fx (x) Find the marginal pdf of Y, fy (y) с. d. P(X>2.5 and Y <1.5) Are X and Y independent? You must demonstrate this using the definition. What is the correlation between X and Y? е. f. g. What is the probability that Y<1.5 given X=0?
Transcribed Image Text:Consider the function fy (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 fry (x, y) a valid pdf. b. Find the marginal pdf of X, fx (x) Find the marginal pdf of Y, fy (y) с. d. P(X>2.5 and Y <1.5) Are X and Y independent? You must demonstrate this using the definition. What is the correlation between X and Y? е. f. g. What is the probability that Y<1.5 given X=0?
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