Question

Suppose () = 1/8 for 0 ≤ ≤ 4 for x being a continuous random variable Is () a probability density function? Prove or disprove.

Answer 1

The expected value of x ; E(x) = 1

Explanation:

F(x) = 1/8 for 0 ≤ x ≤ 4

To prove that it is a probability density function we will find E(x )

attached below is the required prove

It is proven that F(x) = 1/8 for 0 ≤ x ≤ 4 is probability density function

The expected value of X = 1