Question

Let the m.g.f. of a r.v. S equal to

M ( z ) = e x p { 100 ( 1 ( 1 − z 2 ) 2 − 1 ) }.

Suppose that  S = X 1 + . . . + X N, and corresponds to the known

1.Name the distribution of S.

Group of answer choices

Poisson distriution

Gamma distribution

Exponential distribution

Uniform distribution

Compound Poisson

2.What is the expectation of S?

Answer 1

MGF of S is given by M ( z ) = e x p { 100 ( 1 ( 1 − z 2 ) 2 − 1 ) }.

then

1. distribution of S

is Compound Poisson distribtion.

reason:-

since functional form of Mgf of S is given by which corresponds to the given form of S.

2. expectation of S

formula of expectation of S is

from the above equation of mgf we can see that

E(X)=1

so