Moment Generating Functions

Problem 1

mx[t_]:=0.45E^t+0.35E^(2t)+0.15E^(3t)+0.05E^(4t)

mx'[t]

D[mx[t],t]

mx'[0]

mx''[0]

Problem 3 (b)

binomial rv with n = 10, p = 0.5

mx[t_]:=(1/2+E^t/2 )^10

mx[t]

skewness

((mx'''[0]-3mx''[0]mx'[0]+2mx'[0]^3)/((mx''[0]-mx'[0]^2)^(3/2)))