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Omni-MATH / A palindrome is a string that does not change when its characters are written in…

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problem

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 EE be the expected number of nonempty contiguous substrings of SS which are palindromes. Compute the value of ⌊E⌋\lfloor E\rfloor.
Plain-text mathematical notation (without MathML)
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 ⌊E⌋.
Original LaTeX notation
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 $\lfloor E\rfloor$.

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