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 X.

Nann

Nann

Answered question

2021-06-05

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 X.

Answer & Explanation

brawnyN

brawnyN

Skilled2021-06-06Added 91 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 x
fX(x)=f(x,y)dx
=0113(2x+3y)dx
=1301(2x+3y)dx
=13[x2+3xy]01
=13[(1+3y)0]
=3y+13

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