Question

You are given the probability generating function of X: PX(z)=(0.8z+0.2)10 Calculate the coefficient of variation of X.

Answer 1

Var(X)=1.6

Explanation:

Formula for calculating the coefficient of variation for a probability generating function:

Var(X)= PX''(1) + PX'(1) - [PX'(1)]² ........... eq(1)

Now compute each individual term in the above formula.

PX'(z) =
`(10) (0.8) (0.8z + 0.2)^9`

PX'(1) =
`8 (1)^9` = 8

[PX'(1)]² = 64

PX''(z) =
`(9) (8) (0.8) (0.8z + 0.2)^8`

PX''(1) =
`57.6 (1)^8` = 57.6

Substitute all terms back in eq(1)

Var(X)= 57.6 + 8 - 64

Var(X)= 1.6