Two random variables X and Y with joint density function given by:f(x,y)

Albarellak

Albarellak

Answered question

2021-10-21

Two random variables X and Y with joint density function given by:
f(x,y)={13(2x+4y)0x,10elsewhere
Find the marginal density of Y.

Answer & Explanation

SchulzD

SchulzD

Skilled2021-10-22Added 83 answers

The joint density function of random variables X and Y is :
f(x,y)={13(2x+4y)0x,10otherwise
We have to find :
marginal density of y
fY(y)=f(x,y)dy
=0113(2x+3y)dy
=1301(2x+3y)dy
=13[2xy+3y22]01
=13[(2x+32)0]
=4x+36

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