Two random variables X and Y with joint density function given by: f(x,y)=\begin{cases}\frac{1}{3}(2x+4y)& 0\leq x,\leq 1\\0 & elsewhere\end{cases} Find the marginal density of Y.

ruigE

ruigE

Answered question

2021-05-08

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

ottcomn

ottcomn

Skilled2021-05-09Added 97 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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