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Ch05 - Ch 7. prep questions

Analytical Methods for Business (University of Arizona)

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ch05

Student:

1. A random variable is a function that assigns numerical values to the outcomes of a random experiment.

True False

2. A discrete random variable X may assume an (infinitely) uncountable number of distinct values. True False

3. A continuous random variable X assumes an (infinitely) uncountable number of distinct values. True False

4. A probability distribution of a continuous random variable X gives the probability that X takes on a particular value x, P(X = x).

True False

5. A cumulative probability distribution of a random variable X is the probability P(X = x), where X is equal to a particular value x.

True False

6. The expected value of a random variable X can be referred to as the population mean. True False

7. The variance of a random variable X provides us with a measure of central location of the distribution of

X.

True False

8. The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance.

True False

9. A risk-averse consumer may decline a risky prospect even if it offers a positive expected value. True False

10. A risk averse consumer ignores risk and makes his/her decisions solely on the basis of expected value.

True False

11. Given two random variables X and Y, the expected value of their sum, , is equal to the sum of

their individual expected values, . True False

12. A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

True False

13. A binomial random variable is defined as the number of successes achieved in n trials of a Bernoulli process.

True False

14. A Poisson random variable counts the number of successes (occurrences of a certain event) over a given interval of time or space.

True False

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15. We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size N is significantly larger than the sample size n.

True False

16. Which of the following can be represented by a discrete random variable?

A. The number of obtained spots when rolling a six-sided die

B. The height of college students

C. The average outside temperature taken every day for two weeks

D. The finishing time of participants in a cross-country meet

17. Which of the following can be represented by a discrete random variable?

A. The circumference of a randomly generated circle

B. The time of a flight between Chicago and New York

C. The number of defective light bulbs in a sample of five

D. The average distance achieved in a series of long jumps

18. Which of the following can be represented by a continuous random variable?

A. The time of a flight between Chicago and New York

B. The number of defective light bulbs in a sample of 5

C. The number of arrivals to a drive-thru bank window in a four-hour period

D. The score of a randomly selected student on a five-question multiple-choice quiz

19. Which of the following can be represented by a continuous random variable?

A. The average temperature in Tampa, Florida, during a month of July

B. The number of typos found on a randomly selected page of this test bank

C. The number of students who will get financial assistance in a group of 50 randomly selected students

D. The number of customers who visit a department store between 10:00 am and 11:00 am on Mondays

20. What is a characteristic of the mass function of a discrete random variable X?

A. The sum of probabilities over all possible values x is 1.

B. For every possible value x, the probability is between 0 and 1.

C. Describes all possible values x with the associated probabilities .

D. All of the above.

21. What are the two key properties of a discrete probability distribution?

A.

and

B.

and

C.

and

D.

and

22. EXHIBIT 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is 0?

A. 0.10

B. 0.35

C. 0.55

D. 0.65

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23. EXHIBIT 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is greater than 0?

A. 0.10

B. 0.35

C. 0.55

D. 0.65

24. EXHIBIT 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is negative?

A. 0.00

B. 0.10

C. 0.15

D. 0.35

25. EXHIBIT 5-1. Consider the following discrete probability distribution.

Refer to Exhibit 5-1. What is the probability that X is less than 5?

A. 0.10

B. 0.15

C. 0.35

D. 0.45

26. EXHIBIT 5-2. Consider the following cumulative distribution function for the discrete random variable X.

Refer to Exhibit 5-2. What is the probability that X is less than or equal to 2?

A. 0.14

B. 0.30

C. 0.44

D. 0.56

27. EXHIBIT 5-2. Consider the following cumulative distribution function for the discrete random variable X.

Refer to Exhibit 5-2. What is the probability that X equals 2?

A. 0.14

B. 0.30

C. 0.44

D. 0.56

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28. EXHIBIT 5-2. Consider the following cumulative distribution function for the discrete random variable X.

Refer to Exhibit 5-2. What is the probability that X is greater than 2?

A. 0.14

B. 0.30

C. 0.44

D. 0.56

29. We can think of the expected value of a random variable X as .

A. The long-run average of the random variable values generated over 100 independent repetitions

B. The long-run average of the random variable values generated over 1000 independent repetitions

C. The long-run average of the random variable values generated over infinitely many independent repetitions

D. The long-run average of the random variable values generated over a finite number of independent repetitions

30. The expected value of a random variable X can be referred to or denoted as .

A. µ

B. E(X)

C. The population mean

D. All of the above

31. EXHIBIT 5-3. Consider the following probability distribution.

Refer to Exhibit 5-3. The expected value is .

A. 0.9

B. 1.5

C. 1.9

D. 2.5

32. EXHIBIT 5-3. Consider the following probability distribution.

Refer to Exhibit 5-3. The variance is .

A. 0.89

B. 0.94

C. 1.65

D. 1.90

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33. EXHIBIT 5-3. Consider the following probability distribution.

Refer to Exhibit 5-3. The standard deviation is .

A. 0.89

B. 0.94

C. 1.65

D. 1.90

34. EXHIBIT 5-4. Consider the following probability distribution.

Refer to Exhibit 5-4. The expected value is .

A. -1.0

B. -0.1

C. 0.1

D. 1.0

35. EXHIBIT 5-4. Consider the following probability distribution.

Refer to Exhibit 5-4. The variance is .

A. 1.14

B. 1.29

C. 1.65

D. 1.94

36. EXHIBIT 5-4. Consider the following probability distribution.

Refer to Exhibit 5-4. The standard deviation is .

A. 1.14

B. 1.29

C. 1.65

D. 1.94

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37. An analyst has constructed the following probability distribution for firm X's predicted return for the upcoming year.

The expected value and the variance of this distribution are:

A. Option A

B. Option B

C. Option C

D. Option D

38. An analyst believes that a stock's return depends on the state of the economy, for which she has estimated the following probabilities:

According to the analyst's estimates, the expected return of the stock is .

A. 7.8%

B. 11.4%

C. 11.7%

D. 13.0%

39. An analyst estimates that the year-end price of a stock has the following probabilities:

The stock's expected price at the end of the year is .

A. \$87.50

B. \$88.50

C. \$89.00

D. \$90.00

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40. EXHIBIT 5-5. The number of homes sold by a realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the probability that the realtor will sell at least one house during a month?

A. 0.20

B. 0.40

C. 0.60

D. 0.80

41. EXHIBIT 5-5. The number of homes sold by a realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the probability that the realtor sells no more than one house during a month?

A. 0.20

B. 0.40

C. 0.60

D. 0.80

42. EXHIBIT 5-5. The number of homes sold by a realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the expected number of homes sold by the realtor during a month?

A. 1

B. 1.2

C. 1.5

D. 2

43. EXHIBIT 5-5. The number of homes sold by a realtor during a month has the following probability distribution:

Refer to Exhibit 5-5. What is the standard deviation of the number of homes sold by the realtor during a month?

A. 0.56

B. 0.75

C. 1

D. 1.2

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44. EXHIBIT 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the probability that the salesman will sell one car during a week?

A. 0.20

B. 0.40

C. 0.60

D. 0.80

45. EXHIBIT 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the probability that the salesman sells no more than one car during a week?

A. 0.20

B. 0.40

C. 0.60

D. 0.80

46. EXHIBIT 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the expected number of cars sold by the salesman during a week?

A. 0

B. 0.8

C. 1

D. 1.5

47. EXHIBIT 5-6. The number of cars sold by a car salesman during each of the last 25 weeks is the following:

Refer to Exhibit 5-6. What is the standard deviation of the number of cars sold by the salesman during a week?

A. 0.56

B. 0.75

C. 0.80

D. 1

48. A consumer who is risk averse is best characterized as .

A. A consumer who may accept a risky prospect even if the expected gain is negative

B. A consumer who demands a positive expected gain as compensation for taking risk

C. A consumer who completely ignores risk and makes his/her decisions based solely on expected values

D. None of the above

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49. A consumer who is risk neutral is best characterized as .

A. A consumer who may accept a risky prospect even if the expected gain is negative

B. A consumer who demands a positive expected gain as compensation for taking risk

C. A consumer who completely ignores risk and makes his/her decisions based solely on expected values

D. None of the above

50. How would you characterize a consumer who is risk loving?

A. A consumer who may accept a risky prospect even if the expected gain is negative.

B. A consumer who demands a positive expected gain as compensation for taking risk.

C. A consumer who completely ignores risk and makes his/her decisions solely on the basis of expected values.

D. None of the above.

51. EXHIBIT 5-7. An investor has a \$200,000 portfolio of which \$120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.

Refer to Exhibit 5-7. The correlation coefficient between the returns on Stocks A and B is .

A. -0.17

B. 0.20

C. 0.80

D. 4.97

52. EXHIBIT 5-7. An investor has a \$200,000 portfolio of which \$120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.

Refer to Exhibit 5-7. The expected return of the portfolio is .

A. 2.60%

B. 5.04%

C. 7.64%

D. 14.90%

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53. EXHIBIT 5-7. An investor has a \$200,000 portfolio of which \$120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.

Refer to Exhibit 5-7. The portfolio variance is .

A. 8.17%

B. 13.80%

C. 66.78 (%)2

D. 190.70 (%)2

54. EXHIBIT 5-8. An investor has a \$100,000 portfolio of which \$75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.

Refer to Exhibit 5-8. The expected return of the portfolio is .

A. 6.30%

B. 6.75%

C. 7.38%

D. 13.50%

55. EXHIBIT 5-8. An investor has a \$100,000 portfolio of which \$75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table.

Refer to Exhibit 5-8. The standard deviation of the portfolio is .

A. 9.39 (%)

B. 14.19 (%)

C. 88.23 (%)2

D. 201.41 (%)2

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56. Given the information in the accompanying table, calculate the correlation coefficient between the returns on Stocks A and B.

A. -0.212

B. -0.167

C. 0.167

D. 0.212

57. Which of the following statements is most accurate about a binomial random variable?

A. It has a bell-shaped distribution.

B. It is a continuous random variable.

C. It counts the number of successes in a given number of trials.

D. It counts the number of successes in a specified time interval or region.

58. It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective?

A. 0.00729

B. 0.0081

C. 0.081

D. 0.03

59. It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?

A. 0.0010

B. 0.2916

C. 0.3439

D. 0.6561

60. It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?

A. 0.0010

B. 0.2916

C. 0.3439

D. 0.6561

61. Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that none of them has a degree in economics?

A. 0.027

B. 0.300

C. 0.343

D. 0.900

62. Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that at least one of them has a degree in economics?

A. 0.300

B. 0.343

C. 0.657

D. 0.900

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63. EXHIBIT 5-9. On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected.

Refer to Exhibit 5-9. What is the probability that two light bulbs will be defective?

A. 0.0105

B. 0.0746

C. 0.3151

D. 0.5987

64. EXHIBIT 5-9. On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly sele

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