Chapter 15.6, Problem 2P

It is shown in the kinetic theory of gases that the probability for the distance a molecule travels between collisions to be between $x$ and $x+dx$, is proportional to $e^{-x/\lambda }dx,$ where $\lambda$ is a constant. Show that the average distance between collisions (called the "mean free path") is $\lambda$.

Find the probability of a free path of length $\ge 2\lambda$.