Let n E N. Let X1,...,X, be independent random variables uniformly distributed in (1,...,n}. Let Zn...

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Let n E N. Let X1,...,X, be independent random variables uniformly distributed in (1,...,n}. Let Zn = minisaSn-1|X+1 - X. 1. Compute P(Z, = 0). 2. What is the limit of the sequence (P(Zn = 0)),>1? 3. Prove that the sequence (E[Z.]),>i is bounded? Let n E N. Let X1,...,X, be independent random variables uniformly distributed in (1,...,n}. Let Zn = minisaSn-1|X+1 - X. 1. Compute P(Z, = 0). 2. What is the limit of the sequence (P(Zn = 0)),>1? 3. Prove that the sequence (E[Z.]),>i is bounded?