1 . Let $n \geq 2$ be an integer. Consider a string $c_1,c_2,...,c_n$ of length $n$, in which each character $c_i$ is a uniformly random element of the set $\{1,2,3\}$ (independently of all other characters). Consider the random variable $X$ whose value is the number of indices $i \in \{1,...,n - 1\}$ for which the product $c_i \cdot c_{i + 1}$ is odd.

What is the expected value $\mathbb{E}(X)$ of the random variable $X$?

Hint: Use indicator random variables.