⋆ Let random variable X follow the zero-truncated Poisson (λ) d... | Filo
⋆ Let random variable X follow the zero-truncated Poisson (λ) d... | Filo
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(a) Let X have zero-truncated (or decapitated) Poisson distribution with parameter λ = 12. The probability mass function (pmf) of X is given by Pk = PX = k. Show that the probability generating function (pgf) of X is given by P(s) = (e^λs - 1)^-1(e^λs - 1). Also, verify that P(1) = Σ(k-1)Pk = 1. Additionally, show that E(X) = λ and var(X) = λ/(e^λ - 1).
(a) Let X have zero-truncated (or decapitated) Poisson distribution wit…
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