Exercise 3.6 (Negative Binomial Distribution) For the random variable T defined in Exercise 3.5, let X = T − m. Show that

Also, let p = 1 − λ for some λ > 0. Prove that X converges in law to a Poisson random variable as n → ∞.

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P{X=k} = m+k-1Ck pm (1 - p), k = 0,1,....