2.3.3 Suppose that 1; 2; : : : are independent and identically distributed with Prfk D

1g D 1 2 . Let N be independent of 1; 2; : : : and follow the geometric probability mass function

where 0 1 C CN.

(a) Determine the mean and variance of Z.

(b) Evaluate the higher moments m3 D E
Z3
and m4 D E
Z4
.
Hint: Express Z4 in terms of the i’s where 2 i D 1 and E[ij] D 0.

Transcribed Image Text:

PN(k) a(1-a) for k = 0,1,...,