Thread: Turning a mgf into a pmf

this is given m(t) = (1/3) + (2/3)e^t


m (t) = (.25 + .75e^t)^12

How do these become pmf's and also what is the first and second derivative of the first one. Is it just 2/3 e^t?

Originally Posted by wolverine21

this is given m(t) = (1/3) + (2/3)e^t


m (t) = (.25 + .75e^t)^12

How do these become pmf's and also what is the first and second derivative of the first one. Is it just 2/3 e^t? Mr F says: Yes.

Ah yes. The recognition problem.

Big hint: If X ~ Binomial(n, p) then $\displaystyle m_X (t) = [(1 - p) + p e^t]^n$