STAT 599 Spring 2013 Homework 1 -------------------------------- 1. Show all the steps to derive the expression for the normal density function in exponential family form. This is given under the heading "Normal or Gaussian" on page 115 of the book. 2. Show all the steps to derive the expression for the binomial density function in exponential family form. This is given under the heading "Binomial" on page 116 (top) of the book. 3. Derive the variance of a binomial random variable by applying the general formula for var(Y) when Y is in the exponential family, given in the middle of page 116. 4. Do problem 3 (all parts) given on page 53 of the book. 5. Do problem 4(a) given on page 53 of the book. NOTE: Examine all relevant aspects of model building that we have discussed in class, such a goodness-of-fit, model diagnostics, etc. Write a couple of paragraphs summarizing your model and your validation of it. *** For the last two problems, you will have to load the 'faraway' package in R to access the data sets. If you have never installed it, type install.packages("faraway") and follow the directions. To load the package for use in an R session, type library(faraway) Then you can type help(pima) and help(aflatoxin) for details on these two data sets.