Please Answer the following the Question

Let n ( N". Let Xi,.... X,, be independent random variables uniformly distributed in (1, .. . . n). Let Z. = minisign-1 |Xi+1 - Xil. 1. Compute P(Z, = 0). 2. What is the limit of the sequence (F(Z, = 0)),317 3. Prove that the sequence (E[Z,]),, is bounded