To calculate moments of discrete distributions, it is often easier to work with the factorial moments (see
Question:
(a) Calculate the factorial moment E[X (X - 1)] for the binomial and Poisson distributions.
(b) Use the results of part (a) to calculate the variances of the binomial and Poisson distributions.
(c) A particularly nasty discrete distribution is the beta-binomial, with pmf
where n, a, and b are integers, and y = 0,1,2,... ,n. Use factorial moments to calculate the variance of the beta-binomial. (See Exercise 4.34 for another approach to this calculation.)
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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