Homework 7

Due October 21 at midnight

  1. Use the data (0.4, 0.7, 1.1, 1.9, 2.1, 2.9, 3.1, 3.8) and find the MLE estimates of a normal distribution for both the mean and the variance given that data. Restrict the parameters so that the signal to noise ratio is equal to 2. This is equivalent to saying that mu/sigma = 2. Using built-in R functions is okay.
  2. Suppose the data above comes, instead, from a Gamma distribution with unknown parameters alpha and theta where the mean is alpha times theta. You wish to enforce the restriction that alpha < theta as well as restricting each of the parameters to be positive. What are the maximum likelihood estimates of the Gamma parameters under those constraints?
  3. Perform all parts of the problems in Accelerated Testing Case Study.
  4. Submit this homework by committing the necessary files (including any data files) in the appropriate directory and pushing to your central Git repository. Remember to not commit files that are easily reproducible.