Suppose the random variables X and Y have a pdf given byf(x,y)=x+y on 0<x<1, 0<y<1Find F(\frac{1}{4},\frac{1}{2}).

Ernstfalld

Ernstfalld

Answered question

2021-05-17

Suppose the random variables X and Y have a pdf given by
f(x,y)=x+y on 0 Find F(14,12).

 

Answer & Explanation

Bentley Leach

Bentley Leach

Skilled2021-05-18Added 109 answers

Given that,
X and Y are two random variables
The joint pdf of them is given by,
f(x,y)={x+y   0<x<1,0<y<10     otherwise
By definition of cumulative distribution function,
F(x,y)=0x0y(s+t)dtds
=0xs(t)0y+(t22)0yds
=0xsy+y22ds
=y(s22)0x+y22(s)0x
=yx22+xy22
Now, F(14,12)=(12)(14)22+(12)2(14)2=364

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