  The Chernoff bound is a well-known tool for obtaining a high probability
bound on the expectation of a Bernoulli random variable in terms of its sample
average. This bound is commonly used in statistical learning theory to upper
bound the generalisation risk of a hypothesis in terms of its empirical risk on
held-out data, for the case of a binary-valued loss function. However, the
extension of this bound to the case of random variables taking values in the
unit interval is less well known in the community. In this note we provide a
proof of this extension for convenience and future reference.
