If the moment generating function of X is Mt 11 3 t t Solu

If the moment generating function of X is M(t) = 1/1 - 3 t, t

Solution

the given moment generating function is same as that of exponential distribution with theta=1/3

then

E(X)=1/1/3=3

var(X)=9

we have to find P(6.1<X<6.7)

P(6.1<X<6.7)=integrating 1*e^-(1/3)x/3 (limit 6.1 to 6.7)

                    =e^-6.1/3-e^-6.7/3

                           =e^-2.03-e^-2.23

                            =0.1313-0.1075=0.0238