Let X and Y be jointly continuous random variables wth joint PDF is given by: f_{X,Y}(x,y)=2 where 0 \leq y \leq x \leq 1 Show the marginal PDF of X and Y.

Lennie Carroll

Lennie Carroll

Answered question

2021-05-01

Let X and Y be jointly continuous random variables wth joint PDF is given by:
fX,Y(x,y)=2 where 0yx1
Show the marginal PDF of X and Y.

Answer & Explanation

Derrick

Derrick

Skilled2021-05-02Added 94 answers

It is given that X and Y be jointly continuous random variables with joint PDF is given by:
fX,Y(x,y)=2 where 0yx1
We have to find marginal PDF of X and Y.
fX(x)=abf(x,y)dy and fY(y)=abf(x,y)dx
fX(x)=012dy and fY(y)=012dx
fX(x)=2 and fY(y)=2
Thus, the marginal PDF of X and Y are:
fX(x)={2, 0x10, otherwise
fY(y)={2, 0y10, otherwise

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