# Find the cdf of the third smallest among $X_{1},… , X_{8}$

We have $X_{1},... , X_{8}$. All independent exponential r.v. with mean $1$. I know how to find the cdf of the smallest among them, but i didn't see how to find the third smallest and its expected value.

Let $X_{(3)}$ be the third-smallest of $X_1, \ldots, X_8$. Then $X_{(3)} < x$ if and only if at least three of $X_1, \ldots, X_8$ are less than $x$. Now, $P(X_1 < x) = 1 - e^{-x}$ (and similarly for $X_2, \ldots, X_8$). Can you take it from here?