STAT 301.001 Fall 2016, Homework 6 Due: October 7th, Friday at the beginning of class Show your work in the answers. Problems from the textbook All questions from 3-1 to 3-9, and 3-13. You only need to answer \"discrete\" or \"continuous\" for the first 9 problems. Additional Problem 1 Roll a die twice. The sample space for this random experiment is {(x, y)|x, y = 1, 2, . . . , 6} Let X be the number on the first roll, Y be the number on the second roll, and Z be the absolute difference of the two numbers (i.e. Z = |X Y | ). (a) What is the range of Z? (b) Is Z a discrete or continuous random variable? Why? (c) Describe the event {Z 4} by listing all elements in this event. Hint: An event is always a subset of the sample space. (d) Find the pmf and cdf of Z. Additional Problem 2 The following is a pmf of a discrete random variable X, where c is a constant. x f (x) 0 0.15 0.5 0.30 2 0.45 (a) What is the value of c? (b) Find F (1), F (2) and F (3), where F is the cdf of X. (c) Find P (0 < X 1) and P (X > 1). 1 8 c