1 . Let $n \geq 2$ be an integer. Consider a string $c_1,c_2,\dots,c_n$ of length $n$, in which each character $c_i$ is a uniformly random element of the set $\{\alpha, \beta, \gamma, \delta, \epsilon\}$ (independently of all other characters).
Define the random variable $X$ to be the number of indices $i$ with $1 \leq i < n$ for which $c_i = c_{i+1}$.
What is the expected value $\mathbb{E}(X)$ of the random variable $X$?
Hint: Use indicator random variables.