?A random variable X has the discrete uniform distribution \(f(x)=\frac{1}{m}\)

Chapter 5, Problem 5.8.1

(choose chapter or problem)

A random variable X has the discrete uniform distribution

                               \(f(x)=\frac{1}{m}\), \(x=1,2, \ldots, m\)

(a) Show that the moment-generating function is

                          \(M_{X}(t)=\frac{e^{t}\left(1-e^{t m}\right)}{m\left(1-e^{t}\right)}\)

(b) Use \(M_{X}(t)\) to find the mean and variance of X.

Text Transcription:

f(x)=1/m

x=1,2, ldots, m

M_X(t)=e^t(1-e^tm)/m(1-e^t)

M_X(t)