Question 1

Find the expected value of the random variable whose distribution is given below. Round answer to the hundredths place.

Outcome	Probability
- 5	0.2
2	0.3
4	0.4
12	0.1

Expected value =

Question 2

In this remote mountain cabin there is no wireless connection to the outside world. It is snowing heavily outside so you and your brother decide to play tic-tac-toe all day. Whoever wins a game wins $1 from the other person. Suppose you win 68% of the time. What is the expected value of the game from your point of view? Enter answer WITHOUT the $ sign.

Question 3

You sell your hand-made bracelets on the Internet. For each bracelet sold, you make a profit of $18. For each bracelet that's returned for a replacement, you make a profit of $5. For each bracelet that is returned for a full refund, you lose $3. What is your expected profit per bracelet if 7% of your bracelets are returned for replacement and 2% are returned for a full refund? Enter answer WITHOUT the $ sign, and round answer to the hundredths place.

Question 4

There are 12 quizzes in an online class you are taking. If you score 90% on 5 of the quizzes, 80% on 4 of the quizzes, and 70% on 3 of the quizzes, what is your average quiz score? Round answer to a whole number as a percent.

Question 5

Recall that the expected value of a random variable that follows a binomial distribution with parameters n and p equals np (Formula (6.3.1) on page 139 in our book).

An exam consists of 100 multiple choice questions, a robot randomly selects an answer for each question. Find the expected correct number of answers selected by the robot

a) If each question has 4 possible answers and one of them is correct.

b) If each question has 5 possible answers and one of them is correct.

c) If each question has 5 possible answers and two of them are correct.

Question 6

For simplicity, let's assume voters judge a candidate running for a public office by the double S standard: substance and showmanship.

Assume candidate X's substance score is 80 and showmanship score is 30, while candidate Y's substance score is 50 and showmanship score is 70.

50 years ago voters gave substance 90% of weight and showmanship 10% of weight. Today's voters, on the other hand, give substance 20% of weight and showmanship 80% of weight.

a) If X and Y ran against each other 50 years ago, the voters would give X a combined score of , and Y a combined score of , making the winner.

b) If X and Y run against each other today, the voters would give X a combined score of , and Y a combined score of , making the winner.