Let Yn be a binomial random variable with parameters n and p. Assume that a certain set H of positive integers has a density and that this density is equal to d. Prove the following statements:
(a) \lim _{n \rightarrow \infty}P(Y_n\in H)\equal{}d if H is an arithmetic progression.
(b) The previous limit relation is not valid for arbitrary H.
(c) If H is such that P(Yn∈H) is convergent, then the limit must be equal to d.
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