Question

Suppose X has probability density function f(x)=6x(1-x) for 0<x<1 and 0 otherwise. What is E[X] and Var[X]?

Answer 1

`E[X]=1/2` and `Var[X}= 1/20`

Explanation:

`E[X] = int_0^1 6x^2(1-x)dx= 1/2`
and
`E[X^2] = int_0^1 6x^3(1-x)dx= 3/(10)`
So `Var[X]= E[X^2]-(E(X))^2=3/(10)- 1/4=1/20`