it should be max[x_1, ...,,x_n] by using maximum likehood estimation

Given k measurements x_1, x_2, ... x_k, the probability density function for x is P(x) = { 1/d for x in [0,d], 0 otherwise }. d* = argmax{d} (product{i = 1:k} P(x_i) ) = argmax{d} (sum{i = 1:k} log (P(x_i)) ) = argmax{d} (sum{i = 1:k, d >= max (x_i)} log(1) - log(d) ) = argmax{d} (sum{i = 1:k, d >= max (x_i)} -log(d) ) = max(x_i)

d=2Avg(X) / d=2Median(X)

The expectation of max(x_i) is (n-1)d/n, therefore an unbiased estimator would be n*max(x_i)/(n-1)