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A moment generating function does exist for the hypergeometric distribution.
(1/x)e^-(y/x)
See: http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
Using the Taylor series expansion of the exponential function. See related links
The applications of battery at the generating stations is that they are used for applications maintenance and test schedules.
The MGF is exp[lambda*(e^t - 1)].
It is exp(20t + 25/2*t^2).
The derivative of the moment generating function is the expectation. The variance is the second derivative of the moment generation, E(x^2), minus the expectation squared, (E(x))^2. ie var(x)=E(x^2)-(E(x))^2 :)
In a generating station the battery is used to test schedules.
The moment generating function is M(t) = Expected value of e^(xt) = SUM[e^(xt)f(x)] and for the Poisson distribution with mean a inf = SUM[e^(xt).a^x.e^(-a)/x!] x=0 inf = e^(-a).SUM[(ae^t)^x/x!] x=0 = e^(-a).e^(ae^t) = e^[a(e^t -1)]
Your question did not identify one distribution in particular. I have provide in the related link the moment generating functions of various probability distributions.
Energy generating.