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) = [tex](10) (0.8) (0.8z + 0.2)^9[/tex]
PX'(1) = [tex]8 (1)^9[/tex] = 8
[PX'(1)]² = 64
PX''(z) = [tex](9) (8) (0.8) (0.8z + 0.2)^8[/tex]
PX''(1) = [tex]57.6 (1)^8[/tex] = 57.6
Substitute all terms back in eq(1)
Var(X)= 57.6 + 8 - 64
Var(X)= 1.6
