?The geometric random variable X has probability distribution \(f(x)=(1-p)^{x-1} p\)
Chapter 5, Problem 5.8.3(choose chapter or problem)
The geometric random variable X has probability distribution
\(f(x)=(1-p)^{x-1} p\), \(x=1,2, \ldots\)
(a) Show that the moment-generating function is
\(M_{X}(t)=\frac{p e^{t}}{1-(1-p) e^{t}}\)
(b) Use \(M_{X}(t)\) to find the mean and variance of X.
Text Transcription:
f(x)=(1-p)^x-1 p
x=1,2, ldots
M_X(t)=pe^t/1-(1-p)e^t
M_X(t)
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