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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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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 …
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