The joint density of the random variables X and Y is given byf(x,y)=\beg

Trent Carpenter

Trent Carpenter

Answered question

2021-11-03

The joint density of the random variables X and Y is given by
f(x,y)={8xy0x1,0yx0otherwise
Find the conditional density of X
Find the conditional density of Y

Answer & Explanation

smallq9

smallq9

Skilled2021-11-04Added 106 answers

Step 1
We have been given the joint density function of random variables X and Y as,
f(x,y)={8xy0x1,0yx0otherwise
={8xy0x1,0yx0otherwise
The conditional density function of X is computed as,
P(X=xY=y)=f(x,y)f(y)=8xy4y=2x
The conditional density function of Y is computed as,
P(Y=yX=x)=f(x,y)f(x)=8xy4x=2y

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