Let x and y be two continuous random variables whose function is the probability density joint is given by: a)Find the conditional pdf of x given that y = Y,px|y(X|Y): b)Calculate E[x|y = Y], to 0<=Y<=1. c)Calculate Var [ x|y = Y], to 0 <= Y <=

Let x and y be two continuous random variables whose function is the probability density joint is given by: a)Find the conditional pdf of x given that y = Y,px|y(X|Y): b)Calculate E[x|y = Y], to 0<=Y<=1. c)Calculate Var [ x|y = Y], to 0 <= Y <=

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 53CR

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Question

1)Let x and y be two continuous random variables whose function is the probability density joint is given by:

a)Find the conditional pdf of x given that y = Y_,px|y(X|Y):
b)Calculate E[x|y = Y], to 0<=Y<=1.
c)Calculate Var [ x|y = Y], to 0 <= Y <= 1.

Pry (X,Y)= {
6XY, 0≤x≤ 1,0 ≤ y ≤ √X
0, caso contrário.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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