A probability space has four equally likely outcomes in its sample space: N = {1010,0110, 1001, 0101} Let B, be the event '1 in the ith place fori {1,2,3,4}. a) Assign a random variable X to the space such that for a 22, X(a) is the position of the first nonzero digit in a. What is the expected value of X? (2 marks) b) For three events B:,B,, B, state what it means for them to be pairwise independent and mutually independent. (2 marks) c) For which, if any, values of ijare B, B, pairwise independent? (6 marks)