You are given the probability generating function of x: px(z)=(0.8z+0.2)10 calculate the coefficient of variation of x.

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) =

PX'(1) = = 8

[PX'(1)]² = 64

PX''(z) =  

PX''(1) =   = 57.6

Substitute all terms back in eq(1)

Var(X)= 57.6 + 8 - 64

Var(X)= 1.6

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