1. ## confidence intervals

Suppose
X1; : : : ;Xn is a random sample from a Bernoulli distribution with probability P(Xi = 1) = p.
(i) What is the variance of
Xi? Show that the estimator p* = sample meanhas expectation p and find its variance.
(ii) Using the central limit theorem construct a random variable which has an approximate standard normal distribution and indicate how this can be used to find

a 100(1-alpha)%
confidence interval for p.

ok. I have E(sample mean) = p, variance = pq/n. have variance of Xi = pq

so for my confidence interval I have
-z(sqrt(pq))/n + p < sample mean < z((sqrt(pq))/n + p

but how would i rearrange this to get a CI for p?

many thanks

2. Hey, I'm doing the same course as you... I have sqrt(n) instead of n in your confidence interval.

I'm not sure the question is asking for an explicit confidence interval... just to "indicate" how to find one, so what you have so far is probably sufficient.