Suppose the random variables X and Y have a joint pdff_{XY}(x,y)=\begin{cases}x+y & 0\leq x,y \leq 1\\0 & otherwise\end{cases}Find Pr(X>sqrt{Y})

Ava-May Nelson 2021-05-01 Answered

Suppose the random variables X and Y have a joint pdf
fXY(x,y)={x+y0x,y10otherwise
Find Pr(X>Y)

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Expert Answer

Derrick
Answered 2021-05-02 Author has 94 answers
Step 1
Given information:
The joint probability density function of the random variables X and Y is as given below:
fXY(x,y)={x+y. 0x,y10.otherwise
Step 2
Compute the value of P(X>Y):
The marginal probability density function of X is obtained as given below:
fX(x)=yfXY(x,y)dy
=01(x+y)dy
=x[y]01+[y22]01
fX(x)=x+12
The value of P(X>Y) is obtained as given below:
P(X>Y)=y1(x+12)dx
=y1xdx+y112dx
=[x22]y1+[x2]y1
=12y2+12y2
=1y2y2
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