Problem 7. [ti points] Suppose X1,...,J{ ~N[yx,of] and 1'1...,Ym ~ Bernoulliiip} where of is know. 1. [1} 1i.I'Iul'hat does the Law of Large Numbers allow you to assert about in? 1. [1} The Central Limit Theorem says that IE (LaF1) } NM, 1}. Find F3: and or .'r' Assume that in = I135, ?m = 0.3, o; = 9 and that n = m = 35. 3. [2} Construct an approximate 95% Condence Interval for pr Spy. Justify each step; mention the corresponding theorems when necessary. 4. [2] Suppose now that n and m are still equal but unkown. Find the smallest sample size that would allow you to reject the null hypothesis Hg : F: = 3p], in favor of the alternative H1 : F: .: 3y? {your answer does not need to be exact}