550.111, Fall 2014: Homework 2 This homework is due at the beginning of lecture on Friday, September 19, 2014. Y ou are fre e to talk wit h eac h other and get help. However, yo u should write up yo ur own answers and under sta nd every- thing you write. Y ou must show ALL YOUR WORK in order to receive credi t. ANSWERS WITHOUT APPROPRIATE JUSTIFICATION WILL RECEIVE NO CREDIT. Problem 1. MBB, Exercise 2.24, page 69. Y ou should do all five parts of the probl em; for part (a), you can generate the histograms by hand or by using R; either method is fine. Problem 2. MBB, Exercises 4.1 and 4.2, page 130. Problem 3. MBB, Exercise 4.13, page 132. Problem 4. Let Ω be the sample spac e correspond ing to three tosses of a coin. Giv e a ver bal descrip tion of the following events: a) A ={HHH,HHT,HTH,HTT }; b) B= {HHH,HHT,HTH,THH }; Problem 5. (Probability, sample spaces, events) Suppose two four-sided dice (which are known as tet rahedr aldiceand whose faces are marked with the numbers 1, 2, 3, and 4, respectively) are rolled simultaneously and the number on each of the upper faces is recorded. Assume all possible outcomes of the two upper faces are equally likely. Find the probabilities of the following events: a) the maxim um of the two num bers rolled is less than or equal to 2; b) the maximum of the two numbers rolled is less than or equal to 3; c) the maximum of the tw o number s rolled is equal to 3; d) Repeat part c for the maximum equal to 1, 2, and 4. e) If M is the maxim um of the two num bers, then P(M= 1) + P(M= 2) + P(M= 3) + P(M= 4) = 1, check that your answers for c) and d) satisfy this relationship. Problem 6. MBB, Exercises 4.40 (omit (e) and (f)), and 4.41, page 149. Problem 7. MBB, Exercise 4.43, page 150, part (a) only. Problem 8. A surv ey of a group ’s comm uting habits last yea r rev ealed the following a) 27% dro ve a car b) 29% rode th e Metro c) 14% rod e a cit y bus 1
