# Confidence interval for the mean of a bounded non stationary random variableb given N samples

I have a random variable bounded on [0,1]. The mean can be modeled as a random process. Assume the change of the mean |mu_i - mu_{i+1}| is bounded with a known bound. Given N (N is not large) samples (X_1,..., X_N) I want to estimate the upper confidence bound on the mean.

I was unable to find anything in the literature and was hoping someone might have some pointers to relevant research :)