Problem 3 (b)

Let X~Bin(n=10,p=(1/2)). The mgf of X is:

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

Compute the first moment, E(X):

mx'[t]

mx'[0]

Compute the second moment, E((X^2)):

mx''[0]

Compute the second moment, E((X^3)):

mx'''[0]

Now compute the skewness of X:

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

The skewness is zero, which makes sense because the binomial distribution is symmetric when p=(1/2).