Question #1: (10 pts)

Identify each of the following as a discrete or continuous random variable.

(c) Yearly maximum daily amount of ozone in Los Angeles.

(d) Time it takes for a plumber to fix a bathroom faucet.

(e) Number of cars ticketed for illegal parking on campus today.

Question #2 (15 pts)

Two of the integers {1, 7, 13, 16, 19} are chosen at random without replacement. LetXdenote the difference larger minus smaller number. List the distinct values ofXand determine their probabilities. [Write theX-values in ascending order.]

Possible choices

x

Possible choices

x

{ 5,11 }

6

{ 11,20 }

9

{ 5,17 }

12

{ 11,23 }

12

{ 5,20 }

15

{ 17,20 }

3

{ 5,23 }

18

{ 17,23 }

6

{ 11,17 }

6

{ 20,23 }

3

Possible choices

x

Possible choices

x

{ 5,5 }

0

{ 11,20 }

9

{ 5,17 }

12

{ 11,23 }

12

{ 5,20 }

15

{ 17,20 }

3

{ 5,23 }

18

{ 17,23 }

6

{ 11,11 }

0

{ 20,23 }

3

Possible choices

x

Possible choices

x

{ 5,11 }

6

{ 11,20 }

9

{ 5,17 }

12

{ 11,23 }

12

{ 5,20 }

15

{ 17,20 }

3

{ 5,23 }

18

{ 17,23 }

6

{ 11,17 }

6

{ 23,23 }

0

Question #3 (25 pts)

Let the random variableXrepresent the sum of the points in two tosses of a die.

(a) List the possible values ofXto answer the next questions.

(b) For each value ofX, list the corresponding elementary outcomes to answer the next question.

(c) Obtain the probability distribution ofX.

Give exact answers (in fraction form if necessary). Write thex-values in ascending order.

Question #4 (20 pts)

Each week a grocery shopper buys either canned (C) or bottled (B) soft drinks. The type of soft drink purchased in 3 consecutive weeks is to be recorded. If a different type of soft drink is purchased than in the previous week, we sayP(B) = 1/2that there is a switch. LetXdenote the number of switches. Suppose that for each purchaseand the decisions in different weeks are independent. Assign probabilities to the elementary outcomes and obtain the distribution ofX.Write thex-values in ascending order.

Question #5 (20 pts)

In bidding for a remodeling project, a carpenter determines that he will have a net profit of 4000 dollars if he gets the contract and a net loss of 51 dollars if his bid fails. If the probability of his getting the contract is 0.1, calculate his expected return.

Question #6 (10 pts)

Consider Bernoulli trials with success probabilityP=1/8.

Given that the first four trials result in all failures, what is the conditional probability that the next four trials are all successes?Round your answers to 4 decimal places.