Discuss the limits of ..

2. Let the sample space ? = [0, 1] and the probability P on 2 assigns the equal weight on the values {0, 1/3, 2/3, 1}. Define a sequence of events (-1) n 09 An = + 09 / n n for n = 3, 4, ..., and a sequence of random variables Xn = 3 I(A, ). Discuss the limits of A, and X7