Show that EX2 EX2 SolutionAns Varaince of a random variable

Solution

Ans. Varaince of a random variable written as

Var(X)=E(X-mu)^2 and mu=E(X)

Var(X)=E(X^2-2*X*mu+mu^2)

=E(X^2)-2*mu*E(X)+mu^2

=E(X^2)-2*mu^2+mu^2 ,since E(X)=mu

=E(X^2)-mu^2

=E(X^2)-[E(X)]^2 , since E(X)=mu

Var(X)=E(X^2)-[E(X)]^2

Var(X)+[E(X)]^2 =E(X^2)

E(X^2) = Var(X)+[E(X)]^2

Here, the minimum possible value of variance is 0.

Therefor, E(X^2) is greater than or equal to [E(X)]^2