?The continuous uniform random variable X has density function

Chapter 5, Problem 5.8.6

(choose chapter or problem)

The continuous uniform random variable X has density function

                         \(f(x)=\frac{1}{\beta-\alpha}\), \(\alpha \leq x \leq \beta\)

(a) Show that the moment-generating function is

                      \(M_{X}(t)=\frac{e^{t \beta}-e^{t \alpha}}{t(\beta-\alpha)}\)

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

Text Transcription:

f(x)=1/beta-alpha

alpha leq x leq beta

M_X(t)=e^t beta-e^t alpha/t(beta-alpha)

M_X(t)