Suppose the a discrete random variable X has a probability m

Suppose the a discrete random variable X has a probability mass function p(x) = cx for x = 1; 2; 3; 4; 5 and p(x) = 0 for other values of x. Find the value of the constant c such that p(x) is a valid probability mass function.

Let Z = 3X2 + 1. Find Var(Z).

Solution

p(x) = cx

AS total prob = 1 first find c

then find pdf of z

E(Z) = 46

Var(z) = 2746-46^2

= 630