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The Random Variable
Published in X. Rong Li, Probability, Random Signals, and Statistics, 2017
Clearly, a characteristic (or moment generating) function and a PDF are a Fourier (or two-sided Laplace) transform pair: Mx(−ω)=ℱ[p(x)],Mx(−s)=ℒ[p(x)]
Discrete Random Variables
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
Suppose the random variable Y has a moment generating function given by m(t)=15et+25e2t+25e3tFind the mean of Y.Find the variance of Y.
Some Structural Properties Related to the Borel-Taner Distribution and its’ Application
Published in American Journal of Mathematical and Management Sciences, 2023
The moment generating function (m.g.f.) can be seen as a particular form of the p.g.f. in which This function has an advantage over the p.g.f. in the sense that it allows for easy computation of the distribution’s moments. These moments can then be applied to derive a distribution’s mean, variance, skewness and kurtosis. Let be the moment generating function of X for Using the relationship between a moment generating function and a probability generating function, we can see that
PMAC: probabilistic multimodality adaptive control
Published in International Journal of Control, 2020
The proof follows directly from the property that the moment generating function of the sum of independent random variables is the product of the individual moment generating functions, and that the moment generating function of a Gaussian probability distribution function is also of Gaussian form. The details of the proof are provided in Appendix 1.