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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.
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Inversion of Moment-generating functions (aka Laplace transform of prob dist)
The inverse Laplace transform takes place in the complex domain and includes the residue theorem. You can probably do that analytically (as the above forwarded you to Wiki). But usually you can perhap …