See: http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
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The MGF is exp[lambda*(e^t - 1)].
It is exp(20t + 25/2*t^2).
The moment generating function for any real valued probability distribution is the expected value of e^tX provided that the expectation exists.For the Type I Pareto distribution with tail index a, this isa*[-x(m)t)^a*Gamma[-a, -x(m)t)] for t < 0, where x(m) is the scale parameter and represents the least possible positive value of X.
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)]
There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.There are many, many formulae:for different probability distribution functions,for cumulative distribution functions,for moment generating functions,for means, variances, skewness, kurtosis and higher moments.