Number Due Problems Solutions Suggested problems from the new sections to prepare for final: 6.7, Problems 22, 24, 32, 36, 42, 46 Some additional problems solutions 8 12/2 5.6, Problems 38, 40 6.7, Problems 2, 6, 8, 10, 12, 16, 18, 20a solutions 7 11/11 5.6, Problems 18, 20, 24, 28, 31, 32, 36 solutions Also, the proof of Chebyschev's Inequality 6 11/4 5.6, Problems 8, 10, 12, 16, 22, 25 solutions Suggested problems to prepare for midterm: 1.7, Problem 54 2.7, Problems 29, 30, 38, 46, 49, 51, 74 3.5, Problems 3, 8, 9, 13, 14, 22, 31, 35, 42, 48, 52 5.6, Problems 1, 2, 3, 4, 5 Some additional problems solutions 5 10/21 3.5, problems 34, 38, 40, 60, 62, 64, 66 i) Give an example of two random variables X and Y which are independent ii) Give an example of two random variables X and Y which are not independent, and so that the marginal distribution of X is geometric. (Hint: make Y be something simple.) solutions 4 10/14 2.7, problems 40, 44, 50, 52, 62 3.5, problems 2, 6, 10, 15, 18, 23, 24, 27, 28 solutions 3 10/7 1.7, problems 50, 52, 55, 56 2.7, problems 28, 33, 34 i) What is the skew of the binomial distribution with p=1/2? ii) Give an example of a distribution with expectation 0, variance 1, and positive skew. solutions Suggested problems to prepare for midterm: 1.7, problems 20, 21, 31, 34, 36, 39, 44, 47, 48 Some additional problems solutions 2 9/16 1.7, problems 4, 5, 8, 10, 15, 16, 17 2.7, problems 9, 16 i) Suppose we shuffle a deck of cards and deal a poker hand (5 cards). What is the probability we get a full house? ii) You will take the first midterm on the 23rd. Give two different sample spaces which might be appropriate for describing the outcome of this exam. (You don't have to assign probabilities.) solutions 1 9/9 2.7, problems 2, 3, 5, 8, 13, 21, 25, 27 i) 4 people bring gifts to a party to exchange. How many ways are there to distribute the gifts so no person receives the gift they brought? ii) 10 chores need to be allocated among 4 people. How many ways are there to do this? What if the chores need to be allocated relatively fairly, so each person does either 2 or 3 of the chores? iii) n students have the option of going on a field trip. There's no rule about how many go. They could all go. Or none of them could go. Or any amount in between. How many groups of people could go on the field trip? iv) Prove that is equal to 2n. solutions