  One-dimensional topological superconductors harbor Majorana bound states at
their ends. For superconducting wires of finite length L, these Majorana states
combine into fermionic excitations with an energy $\epsilon_0$ that is
exponentially small in L. Weak disorder leaves the energy splitting
exponentially small, but affects its typical value and causes large
sample-to-sample fluctuations. We show that the probability distribution of
$\epsilon_0$ is log normal in the limit of large L, whereas the distribution of
the lowest-lying bulk energy level $\epsilon_1$ has an algebraic tail at small
$\epsilon_1$. Our findings have implications for the speed at which a
topological quantum computer can be operated.
