Question: Let X1, X2, . . . be a sequence of i.i.d. random variables having the normal distribution with mean and variance 2. Let n

Let X1, X2, . . . be a sequence of i.i.d. random variables having the normal distribution with mean μ and variance σ2. Let n = 1/n be the sample mean of the first n random variables in the sequence. Show that Pr(|n − μ| ≤ c) converges to 1 as n→∞. Write the probability in terms of the standard normal c.d.f. Φ and use what you know about this c.d.f.

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