Problem bank

Problem 43 of 333MediumStatisticsP043

MLE for Uniform[0, θ]

  1. X1,…,Xn∼Uniform[0,θ]X_1, \ldots, X_n \sim \text{Uniform}[0, \theta]. Find the MLE of θ\theta. Is it unbiased? Find an unbiased estimator with smaller variance than the method-of-moments estimator 2Xˉ2\bar{X}.