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. Are X and Y independent?

Erin Larsen

Erin Larsen

Open question

2022-08-17

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. Are X and Y independent?

Answer & Explanation

Lina Watson

Lina Watson

Beginner2022-08-18Added 9 answers

Since the joint PDF of X and Y can not be written as the product of some two PDFs, we can conclude that X and Y are not independent.
Result:
No.

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