order statistics

• How to Find a Confidence Interval for a Uniform Distribution
  For independent Uniform(0, θ) data, use the sample maximum to derive an exact confidence interval, with formulas and a worked 95% example.
• What Is the MLE for a Uniform(θ, 0) Distribution?
  For iid data from Uniform(θ, 0) with θ < 0, the likelihood is maximized at the sample minimum; if endpoints are reversed, it is the maximum.
• What Is the MLE of θ for a Uniform(0, θ) Distribution?
  For an i.i.d. sample from Uniform(0, θ), the maximum likelihood estimate is the largest observation, because the likelihood decreases for θ above that value.
• What Are the Properties of the Maximum and Minimum of Exponential Random Variables?
  For independent exponential variables, the minimum is exponential with summed rate; derive the maximum's CDF, density, mean, and variance.