4. Let 1 A be the indicator of event A. That is, the random variable 1 A takes the value 1 if A occurs and is 0 if A occurs. (a) What is the support of 1 A? (b) What is the p.m.f. of 1 A? (c) Compute E[ 1 A] (d) What should the subscript of the indicator r.v. on the r.h.s. of the fol- lowing equation be so that equality holds? 1A+1B - 1AB = 17. You may assume that A and B are events. (e) Take the expected value of each side, and you end up with what familiar equation? 5. Let X be a nonnegative, integer-valued random variable. (a) Simplify K=0 (When X (w) =0, then interpret K=0 as 0.) (b) Simplify 21 (x>k). 2