The exponential time hypothesis asserts that an algorithm for SAT must take time $2^{\Omega(n)}$. If I am reading this right, this refers only to deterministic algorithms.
Is it possible that ETH holds, yet their is a random algorithm in time $2^{o(n)}$? If so, is there any name for the hypothesis that any randomized (say BPP-type) algorithm takes time $2^{\Omega(n)}$ as well?