Let $r_n$ be a random variable that returns one of the digits $2, 0, 1, 6$ each with equal probability for all positive integers $n$. Find the value of
$$\mathcal{V}=\mathbb{E} \left[ \sum_{n=1}^{\infty} \frac{r_n}{10^n} \right]$$
where $\mathbb{E}$ denotes the expected value of $x$.
Solution
$$\mathcal{V}=\mathbb{E} \left[ \sum_{n=1}^{\infty} \frac{r_n}{10^n} \right]$$
where $\mathbb{E}$ denotes the expected value of $x$.
Solution
