Question

10. If the moment-generating function of X is find the mean. variance. and omf of X.

Answer 1

as we know that moment generating function M_x(t) = $\sum$ P(x)e^tx

comparing given mgf to above:

\below is pmf of X:

P(X=1)=2/5

P(X=2)=1/5

P(X=3)=2/5

mean E(X) = $\sum$ xP(x)=1*(2/5)+2*(1/5)+3*(2/5)=10/5=2

E(X²)= $\sum$ x²P(x)=1²*(2/5)+2²*(1/5)+3²*(2/5)=24/5=4.8

hence Variance =E(X²)-(E(X))² =4.8-2² =0.8