Multiple Choice

Select the best answer from the available choices foreach question.

1.   Which of the following is NOT part of thedefinition of a sample space S?

•   S can be discrete or continuous

•   Each outcome must be in S at most once

•   Each element in S is equally likely

•   Each outcome must be in S at least once

•   S is a set of possible outcomes in anexperiment

2.   Three A’s, three B’s, and two C’s are arranged atrandom in a row. What is the probability that the letters on bothends are different?

•   0.01

•   0.25

•   0.75

•   0.99

•   None of the above

3.   When constructing this exam, Diana and Audreymade a question bank of 40 Multiple Choice questions (you get 15),30 True/False questions (you get 10), 30 Identify the Distributionquestions (you get 10), and 4 versions of each of the 5 Long Answerquestions. Assuming the order of the questions does not matter, howmany different exams could be created?

  
•   4.029 x 10^10
  
•   5.260 x 10^22
  
•   3.718 x 10^28
  
•   6.403 x 10^53
  
•   none of the above

4.   Three people independently choose one of fivesections of a course to enroll in. What is the probability that atleast two enroll in the same section?

  
•   0.28
  
•   0.48
  
•   0.52
  
•   0.72
  
•   None of the above

5.   Three people are acting in a play. Character Ahas 50% of the lines, Character B has 40%, and Character C has 10%.Each person has a different probability of making a mistake on anyline, independently: 0.03 for A, 0.07 for B, and 0.20 for C. Giventhat a mistake occurred, what is the probability that it was C’sline?

  
•   0.02
  
•   0.063
  
•   0.317
  
•   0.444
  
•   None of the above

6.   Which matches the conditions for using a Binomialapproximation to the Hypergeometric?

  
•   N must be large and n must be small relative toN
  
•   The sampling must be done with replacement
  
•   n must be large and r/N must be small
  
•   Two or more of the above
  
•   None of the above

7.   Suppose the amount of data you use on your phone(in units of 100 MB) has a Poisson distribution with mean 8 permonth. You pay $15 per month plus $3 per 100 MB of data. Find thestandard deviation of a random month's phone bill.

•   6.245

•   8.485

•   9.327
  
•   72
  
•   None of the above

8.   The amount of time a user plays Animal Crossinghas an Exponential distribution with mean 30 minutes. Given thatthe user has been playing for 1 hour, what is the probability theywill still be playing half an hour later?

•   0.012

•   0.135

•   0.368

•   0.632

•   None of the above

9.   Which of the following 4 statements is FALSE?

  
•   If X~Y (i.e. X and Y have the same distribution),then they have a correlation of 1
  
•   If X and Y are independent, they have a correlationof 0

•   If X and Y have a correlation of 0, and Y and Zhave a correlation of 1, then X and Z have correlation of 0

•   Correlation tells us the strength and direction ofthe linear relationship between two variables, whereas covarianceonly tells us the direction

•   Two or more of the above are false

10.   Which of the following 4 statements is TRUE?

•   If X and Y have a negative correlation, they areindependent

•   If X and Y have a correlation of 0, they areindependent

•   If X and Y have a positive correlation, and Y andZ have a positive correlation, then X and Z have positivecorrelation

•   If X = -0.5Y, then the correlation of X and Y is-1

•   Two or more of the above are true

11.   Which of the following 4 statements isFALSE?

  
•   The Normal distribution has mean, median, and modeall equal to μ   

•   A Normal random variable with a larger variancehas a smaller maximum height of its pdf

•   Approximately 95% of the area under the StandardNormal pdf is between -1 and 1

•   The cdf F(x) of a Normal random variable isstrictly increasing for all Real values of x

•   Two or more of the above are false

12.   The return on stock X has mean 5 and standarddeviation 3. The return on stock Y has mean 8 and standarddeviation 10. The standard deviation of an equal portfolio of thetwo stocks (that is, 0.5X + 0.5Y) is 24.25. What is the correlationbetween X and Y?

•   -0.2
  
•   0

•   0.2

•   0.4
  
•   None of the above

13.     Suppose the length in cm of a malesoccer player's foot follows a Normal distribution with mean 30 andvariance 25. Suppose the length in cm of a female soccer player'sfoot follows a Normal distribution with mean 26 and variance 16. Amale and female soccer player are selected at random. What is theprobability the female player has a longer foot than the maleplayer?

•   0.09

•   0.27

•   0.33

•   0.73

•   0.91

14.   Independently of one another, a randomlysurveyed individual can be a non-smoker, a light smoker, or a heavysmoker with probabilities 60%, 30% and 10%, respectively. Supposewe randomly survey a sample of 100 people. Given that 37 of themare light smokers, what is the expected number of heavysmokers?

•   6.3

•   9

•   27

•   54

•   None of the above

15.   The Princess Theatre has 280 seats. 200 ticketsare sold for the new popular movie: The Attack of the Goose.Despite every attendee having an assigned seat, they all decide tosit in seats at random. Find the variance of the number of peoplesitting in their assigned seat. (Hint: use indicator variables)

•   0.712

•   0.714

•   5.246

•   11.704

•   None of the above