MATH 230A Midterm: Math 230A Midterm Fall 2015
Document Summary
Please, mark clearly the beginning and end of each problem. You have 3 hours but you are not required to solve all the problems! Just solve those that you can solve within the time limit. Points assigned to each problem are indicated in parenthesis. I recommend to look at all problems before starting. For any clari cation on the text, one of the tas will be outside the room. You cannot use computers, and in particular you cannot use the web. You can cite theorems (propositions, corollaries, lemmas, etc. ) from amir dembo"s lecture notes by number, and exercises you have done as homework by number as well. Problem 1 (20 points) (a) let x be a random variable taking values in r. prove that, for each > 0, there exists x0 r such that. P(cid:0)x [x0 , x0 + ](cid:1) > 0 . (b) let x, y be independent and identically distributed. P(cid:0)|x y | (cid:1) > 0 .