00:02
Okay, so now i want to clarify certain things.
00:07
So, x follows the independent bernoulli random variable with parameter p.
00:17
So this means p equals 1 equals p, p equals 0 equals 1 minus p.
00:27
And we define y as the sample average of x.
00:36
So some of the properties of xi's are e of xi equals p, variance of xi equals p times 1 minus p.
00:47
Now the central limit theorem states that if x1 through xn are iid random variables with mean mu and variance sigma squared, then as n goes to infinite, we have square root of n, 1 over n, xi minus mu converges in distribution to n, 0, sigma squared.
01:15
So this is called lindbergh -liebe clt.
01:22
Okay, so for our bernoulli case, we have mean of p and variance of p times 1 minus p.
02:04
So according to the clt, so this is yn, this distribution converges in distribution to a normal distribution with mean 0 and variance p times 1 minus p.
02:22
So that proves it.
02:26
And okay, for b, so we can use the delta method here, which is an application of the central limit theorem to functions of random variables...