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

Answer:

Var(X)=1.6

Step-by-step 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