Let A be an array of size n containing the numbers 1, . . . , n in some order. If A[i] and A[i + 1] differ by one then (i, i + 1) is called a pair of neighbors. Suppose that the elements of A form a uniform random permutation of 1, . . . , n. Use indicator random variables to determine the expected number of pairs of neighbors. For example, the array [53124] contains one pair of neighbors, (3, 4), as A[3] and A[4] differ by one.

Hint: consider the events that A[i] and A[i + 1] differ by one.