Expected ranks among mixed exponentials

Let $X, Y_1, Y_2$ be independent random variables such that $X$ has the probability density function $f(x) = \begin{cases} 2 e^{-2x} & \text{if } x \ge 0 \ 0 & \text{otherwise} \end{cases}$ and $Y_1$ and $Y_2$ are identically distributed with probability density function $g(x) = \begin{cases} e^{-x} & \text{if } x \ge 0 \ 0 & \text{otherwise} \end{cases}$. For $i = 1, 2$, let $R_i$ denote the rank of $Y_i$ among $X, Y_1, Y_2$. Then $E(R_1 + R_2)$ equals