Question: In this problem, consider a skip list with n >= 2 elements. As described in class, the height (number of levels) of each node is

In this problem, consider a skip list with n >= 2 elements. As described in class, the height (number of levels) of each node is randomly determined. For simplicity, assume that n is a power of 2 (i.e. log2 n is an integer). Let M be the maximum level of all nodes. (log2 means log_2)

1. Compute the probability that one specific node has at least k*log2 n + 1 levels. 2. Prove that Pr[M >= log2 n + 1] is at least 1

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