Question: 2. For n 1, let Xn be a binomial random variable with parameters n and p. Since Xn is the number of successes in

2. For n ≥ 1, let Xn be a binomial random variable with parameters n and p. Since Xn is the number of successes in n independently performed Bernoulli trials, Xn is the fraction of successes in the first n trials. Show that Xn converges to p in probability.

That is, for all ε > 0,

11-00 n lim P P(x-p|> c) = 0. =

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