Calculation of Expectations
Many of the hardest problems in applied probability revolve around the calculation of expectations of one sort or another. On one level, these are merely humble exercises in integration or summation. However, we should not be so quick to dismiss the intellectual challenges. Readers are doubtless already aware of the clever applications of characteristic and moment generating functions. This chapter is intended to review and extend some of the tools that probabilists routinely call on. Readers can consult the books [34, 59, 60, 78, 80, 166] for many additional examples of these tools in action.
KeywordsDirichlet Distribution Probability Generate Function Factorial Moment Positive Random Variable Gamma Density
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