# Discrete random variable - probability function

## Discrete random variable - probability function

The discrete random variable X has the probability function

$P\left&space;(&space;X=x&space;\right&space;)=\left\{\begin{matrix}&space;kx&space;&&space;x=2,4,6\\&space;k(x-2)&&space;x=8\\&space;0&&space;\text{otherwise}&space;\end{matrix}\right.$

where k is a constant.

(a) Show that k=$\inline&space;\frac{1}{18}$

(b) Find the exact value of F(5).

(c) Find the exact value of E(X).

(d) Find the exact value of E(X2).

(e) Calculate Var(3-4X) giving your answer to 3 significant figures.

MathsTutor4You