Let X and Y be continuous random variables with joint density function f(x,y)={x/5+cy 0<x<1, 1<y<5 0, otherwise, where c is a constant. What is the value of c?

Licinilg

Licinilg

Open question

2022-08-20

Let X and Y be continuous random variables with joint density function
f(x,y)={x5+cy0<x<1,1<y<50otherwise
where c is a constant. What is the value of c?

Answer & Explanation

Harmony Horn

Harmony Horn

Beginner2022-08-21Added 11 answers

Since it has to be R2 f=1, we have that
1=0115(x5+cydy)dx=01(4x5+12c)dx=25+12c
which yield that c=120.
Result:
c=120

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