Suppose $1, $2, ... are iid random variables having mean / and variance o'. Form the random sum SN = $1 + . . . + EN. (a) Derive the mean and variance of Sy when N has a Poisson distribution with parameter (b) Determine the mean and variance of S'w where N has a geometric distributions with mean 1 = 1-p. P (c) Compare the behaviors in (a) and (b) as 1 - co