Let X1, . ,Xn be i. Bernoulli with parameter pie. Let Yn =SUM (i=1 to n)Xi.

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...