Suppose that we wish to test the hypotheses (9.8.1). Let the loss function have the form of (9.8.2). a. Prove that the posterior probability of = 0 is 0f0(x)/[0f0(x) + 1f1(x)]. b. Prove that a test that minimizes r() also minimizes the posterior expected value of the loss given X = x for all x. c. Prove that the following test is one of the tests described in part (b): reject H0 if Pr(H0 true|x) w1/(w0 + w1

Chapter 2, Part One: Frequency Distributions, Histograms, and Related Topics 1. Frequency Distribution: paritions data into classes and assigns each class a frequency a. Frequency Tables: displays information in a frequency distribution, by listing each class along with its frequency b. Constructing a Frequency Table i. Decide on a number of classes between 5 and 15 ii. Calculate the class width 1. (Highest ValueLowest Value) / (# of Classes) a. (# of Classes) What was chosen in step one b. then,