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Moment generating function (MGF)

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Functional invariance of exponential stochastic order

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Moment Generating Function for Brownian motion's exit of interval.

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Existence of a global maximum of a function defined with the moment-generating function

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Bounding the expectation of a function of a zero-mean random variable

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For zero-mean r.v. $X$ with var. $\sigma^2$, want to show $E[e^{2X}]\leq e^{2\sigma^2}$.

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What is the meaning of the cumulant generating function itself?

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#probability-theory #generating-functions #moment-generating-functions
69
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Probability involving a moment generating function

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#probability #random-variables #moment-generating-functions #independence
135
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I have some questions related to Fisher's book 1925.

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#statistics #moment-generating-functions
166
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Conditions for the existence of moments of the supremum of a random variable

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#random-variables #supremum-and-infimum #moment-generating-functions
199
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Given the moment generating function of a continuous-type r.v, how to find the p.d.f?

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#probability-distributions #improper-integrals #moment-generating-functions
95
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Finding a transform of X

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#probability #statistics #moment-generating-functions
189
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Is m.g.f. non-decreasing?

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#moment-generating-functions
158
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Independence of a hitting time and the underlying stochastic process

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#brownian-motion #stochastic-analysis #stopping-times #moment-generating-functions #independence
92
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Upper bound for the $t$-th moment in terms of lower moments

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#probability-theory #statistics #inequality #analytic-number-theory #moment-generating-functions

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