The joint density of the random variables X and Y is given by f(x,y)=\begin{cases}8xy & 0\leq x\leq 1, 0\leq y \leq x\\0 & otherwise\end{cases} Find the marginal density of X

banganX

banganX

Answered question

2021-06-02

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

Answer & Explanation

Arham Warner

Arham Warner

Skilled2021-06-03Added 102 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 marginal density function of X is computed as,
f(x)=01f(x,y)dy
=018xydy
=8x[y22]01
=4x

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