Please provide Handwritten answer

Advanced Math

This a question about Probability and Measure

Let X1 be a random variable that takes value 1 with probability 1/2 and value -1 with probability 1/2. For every i > 1, define the random variable Xi = X1. Clearly, EX; = 0 for all i, so one might hope that the strong law of large numbers says - Sn -> 0 almost surely. However, it can be seen that for each n, P (ISn = 0) = 0, so the almost sure convergence of the SLLN doesn't hold. Which assumption doesn't hold