Let Z Gamma(a, ), where a is an integer. Conditional on Z = z, let X
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Let Z ∼ Gamma(a, λ), where a is an integer. Conditional on Z = z, let X ∼ Pois(z). Show that X has a negative binomial distribution with the following interpretation. For k = 0, 1, . . . , P(X = k) is equal to the number of failures before a successes in a sequence of i.i.d. Bernoulli trials with success parameter λ/(1 + λ).
DistributionThe 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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