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A moment generating function does exist for the hypergeometric distribution.
To derive the moment generating function of an exponential distribution, you can use the definition of the moment generating function E(e^(tX)) where X is an exponential random variable with parameter λ. Substitute the probability density function of the exponential distribution into the moment generating function formula and simplify the expression to obtain the final moment generating function for the exponential distribution, which is M(t) = λ / (λ - t) for t < λ.
See: http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
Using the Taylor series expansion of the exponential function. See related links
The MGF is exp[lambda*(e^t - 1)].
The applications of battery at the generating stations is that they are used for applications maintenance and test schedules.
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 :)
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)]
In a generating station the battery is used to test schedules.
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.