HMMT November 2019 U28

A palindrome is a string that does not change when its characters are written in reverse order. Let $S$ be a 40 -digit string consisting only of 0 's and 1 's, chosen uniformly at random out of all such strings. Let $E$ be the expected number of nonempty contiguous substrings of $S$ which are palindromes. Compute the value of $\lfloor E\rfloor$.