If Mxt 13 23et4 If Mxt 13 23et4 Find PX 3 SolutionX fo

If M_x(t) = (1/3 + 2/3(e^t))⁴

If Mx(t) = (1/3 + 2/3(e^t))^4 Find P(X > = 3)

Solution

X follows Binomial distribution with n=4 and p=2/3

P(X=x)=4Cx*(2/3)^x * (1/3)^(4-x) for x=0,1,2,3,4

So P(X>=3) = P(X=3)+P(X=4)

=4C3*(2/3)^3 * (1/3)^(4-3) + 4C4*(2/3)^x * (1/3)^(4-4)

=0.5925926