2019 November 11,

Math 265: Day 24

Carleton College, Joshua R. Davis

A. Let X₁, X₂, X₃, ... be IID. Let S_n = X₁ + ... + X_n. Compute the MGFs of S_n and S_n / n.

B. Use your answer to the preceding problem to compute the MGF of the average of n independent random variables X_i ~ Unif(a, b).

C. For all n ≥ 0, find the nth moment of X ~ Expo(1). (Hint: Work out the first few and find the pattern.)

D. Find the moment generating function for X ~ Pois(λ).

E. Section 6.10 Exercise 19.