To approximately estimate the pdf p(x) of a random variable/vector x, one way is to divide the domain of x into xed regions, for which the density p(x) takes the constant value hi over the ith region with its volume denoted i. Suppose we have a set of N observations of x such that ni of these observations fall in region i. Using a Lagrange multiplier to enforce the normalization constraint of the pdf, derive an expression for the maximum likelihood estimator for such a histogram-based approximation of the pdf {hi}.