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Any idea on how to solve this challenging problem?
You are given an integer $$$n$$$. Let $$$S$$$ be the set of all strings of length $$$n$$$ that contain only lowercase Latin characters. So $$$S$$$ will have $$$26^n$$$ elements.
You pick a random string $$$s$$$ from set $$$S$$$, then you pick a random index $$$i$$$ from the range $$$[2, n]$$$. What is the expected value of $$$z_i$$$, where $$$z_i$$$ is the value of the $$$Z$$$-function of $$$s$$$ at index $$$i$$$?
