8 For the following named distributions find the value of EX

8. For the following named distributions, find the value of E[X2].

(a) Binomial with parameters n, p.

(b) Uniform with parameters a, b.

(c) Normal with parameters m, variance

Solution

(a) Binomial with parameters n, p.

V(x)=npq = E[X²]- E[X]²   THEREFORE   E[X²]= npq+ (np)²   where np=E[X] and q=1-p

(b) Uniform with parameters a, b.

V(x)= (b-a)²/12 = E[X²]- E[X]²   therefore  E[X²]= (a+b)/2 + (b-a)²/12 where E[X]=(a+b)/2

(c) Normal with parameters