[Math] Expected value of random permutation

Question

Let n ≥ 1 be an integer and consider a uniformly random permutation
$a_1$, $a_2$, . . . ,$a_n$ of the set {1, 2, . . . , n}. Define the random variable X to be the number of indices i for which 1 ≤ i < n and $a_i$ < $a_{i+1}$.
Determine the expected value E(X) of X. (Hint: Use indicator random variables.)

This question seems to be over my head. Any help to lead in right direction is appreciated. Thank you.

Answer 1

Hint: write $X$ as a sum of indicator random variables, and use the fact that they are identically distributed.