Exponential distribution

• How to Test the Mean of an Exponential Distribution
  Test an exponential population mean with an exact chi-square statistic, and use the same pivot to construct a confidence interval for the mean.
• What Is the Expected Maximum of Two Exponential Variables?
  For independent exponential variables with rates λ₁ and λ₂, the expected maximum is 1/λ₁ + 1/λ₂ − 1/(λ₁ + λ₂).
• Conditional Mean and Variance of an Exponential Random Variable
  For an exponential random variable conditioned to exceed a threshold, memorylessness gives a shifted exponential: mean threshold plus 1/rate and variance 1/rate squared.
• How to Find the Mean and Variance of an Exponential Distribution
  For an exponential distribution with rate λ, the mean is 1/λ and the variance is 1/λ²; see the derivation and scale-parameter version.
• How to Find the UMVUE of an Exponential Parameter
  For an i.i.d. exponential sample, the UMVUE depends on whether theta is the scale or rate: use the sample mean for scale and (n−1)/sum Xi for rate.
• What Is the Fisher Information for an Exponential Distribution?
  For an exponential distribution, Fisher information is 1 over the squared rate per observation, or n over the squared rate for n iid observations.
• How to Find an Exponential Percentile on a TI-84
  Find an exponential-distribution percentile on a TI-84 using the inverse CDF, with rate-versus-mean formulas and a worked keystroke example.
• 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.
• What Is the Standard Deviation of an Exponential Distribution?
  For an exponential distribution with rate λ, the standard deviation is 1/λ; with scale θ or mean μ, it equals θ or μ. See the derivation and example.