Transcription of Lecture 6 Moment-generating functions
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Lecture 6 Moment-generating functions
Lecture6: Moment-generating functions1of11 Course:Mathematical StatisticsTerm:Fall2017 Instructor:Gordan itkovi cLecture6 Moment-generating and first propertiesWe use many different functions to describe probability distribution (pdfs,pmfs, cdfs, quantile functions , survival functions , hazard functions , etc.) Moment-generating functions are just another way of describing distribu-tions, but they do require getting used as they lack the intuitive appeal ofpdfs or function (mgf)of the (dis-tribution of the) random variableYis the functionmYof a real param-etertdefined bymY(t) =E[etY],for allt Rfor which the expectationE[etY]is well is hard to give a direct intuition behind this definition, or to explain atwhy it is useful, at this point.
Sep 25, 2019 · Indeed, the mfg of the expo-nential function is defined only for t < 1 t. We will not worry too much for about this, and simply treat mgfs as expressions in t, but this fact is good to keep in mind when one goes deeper into the theory. The fundamental formula for continuous distributions becomes a sum in
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