Given X1,···,Xn ∼Bernoulli(p), and Y1,···,Ym ∼Bernoulli(q), find the plug-in estimator and estimated standard error for p. Recall the definition of the distribution of a Bernoulli random variable, with standard formulae. Find the plug-in estimator and standard error for p − q, and then find an approximate 90% confidence interval for p − q.

Suppose that a random variable Y is an observation from a normal distribution with unknown mean μ and variance σ2 = 1. Find a 95% confidence interval for μ using the Normal Method.