Let X1, . . . ,Xn be i.i.d. Bernoulli with parameter pie. Let Yn =SUM (i=1 to n)Xi.Show that as n –> infinity and pie –> 0 in such a way that npie –> theta > 0, Yn –>d –> Zwhere Z has a Poisson distribution with parameter theta.. Let us define . Hence, is sum of Bernoulli trials each with probability . So, By definition of Binomial distribution, we can saythat follows Binomial distribution with parameters andHence, for…
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