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Unit 5: Probability - Practice Quiz

CSE333 — Combinatorial Studies-I 60 Questions
0 Correct 0 Wrong 60 Left
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1 What is a random variable?

random variables Easy
A. A complete list containing only impossible outcomes
B. A fixed value that never depends on an experiment
C. A numerical value assigned to each outcome of a random experiment
D. A numerical procedure that always produces the same outcome under every condition

2 Which of the following is a discrete random variable?

random variables Easy
A. The number of heads in five coin tosses
B. The exact time required to finish a race
C. The exact height of a student
D. The temperature measured continuously throughout an entire day

3 In a discrete uniform distribution, how are the probabilities of the possible outcomes related?

uniform distribution Easy
A. All outcomes have equal probability
B. Earlier outcomes have higher probability
C. Later outcomes have higher probability
D. Each outcome has a probability determined by its distance from the mean

4 A fair six-sided die follows a discrete uniform distribution. What is the probability of rolling a ?

uniform distribution Easy
A.
B.
C.
D. because the desired face is labeled with the number

5 What is the usual shape of a normal distribution?

normal distribution Easy
A. Strictly decreasing
B. Irregular and strongly skewed toward both ends of the horizontal axis
C. Bell-shaped and symmetric
D. Flat and rectangular

6 For a normal distribution, which statement about the mean, median, and mode is correct?

normal distribution Easy
A. They are equal
B. They are always different because each measures a separate feature of the data
C. The mode is smallest
D. The mean is largest

7 The exponential distribution is commonly used to model which type of quantity?

exponential distribution Easy
A. Waiting time between events
B. Number of events in an interval
C. Outcome of a single coin toss
D. The categories assigned to observations in a nonnumerical survey

8 The Poisson distribution is commonly used to model what?

Poisson distribution Easy
A. The continuously measured heights of all people in a large population
B. The number of events in a fixed interval
C. The outcomes of a fair die
D. The waiting time until one event

9 If has a Poisson distribution with parameter , what is its mean?

Poisson distribution Easy
A.
B. , provided that the events occur independently
C.
D.

10 Which condition is required for a binomial experiment?

binomial distribution Easy
A. Each trial must produce a continuous measurement from a symmetric distribution
B. The number of trials must be unlimited
C. Each trial has two possible outcomes
D. The trials must have unequal probabilities

11 What is the mean of a binomial distribution with parameters and ?

binomial distribution Easy
A.
B.
C.
D. , which is also commonly used as the formula for its variance

12 What is the arithmetic mean of the values ?

mean Easy
A.
B. , obtained by adding the values without dividing by their number
C.
D.

13 Which formula gives the arithmetic mean of observations ?

mean Easy
A.
B.
C.
D.

14 What is the median of the ordered data set ?

median Easy
A.
B.
C. , because this value is obtained by adding every observation in the set
D.

15 What is the mode of the data set ?

mode Easy
A. , because it is the greatest observation appearing in the data set
B.
C.
D.

16 What does a small standard deviation indicate?

standard deviation Easy
A. The values are far from the mean
B. Every value is greater than the mean by exactly the same positive amount
C. The mean is necessarily zero
D. The values are close to the mean

17 Which notation represents the probability of event given that event has occurred?

conditional probability Easy
A.
B.
C.
D. , which instead reverses the condition and the event of interest

18 If and , what is ?

conditional probability Easy
A.
B.
C.
D. , found by adding the intersection probability to the probability of

19 What is Bayes theorem mainly used to calculate?

Bayes theorem Easy
A. The number of equally likely outcomes in every possible random experiment
B. The spread of observations
C. The average of a data set
D. A reversed conditional probability

20 Which formula correctly states Bayes theorem when ?

Bayes theorem Easy
A.
B.
C.
D.

21 A discrete random variable takes values , , and with probabilities , , and , respectively. If , what is ?

random variables Medium
A.
B. , because the largest value of is used
C.
D.

22 A random variable is uniformly distributed on . What is ?

uniform distribution Medium
A.
B.
C.
D.

23 Test scores are normally distributed with mean and standard deviation . Approximately what percentage of scores lie between and ?

normal distribution Medium
A. , using the interval within two standard deviations
B.
C.
D.

24 The lifetime of a component is exponentially distributed with a mean of years. Given that it has already lasted years, what is the probability that it lasts at least more years?

exponential distribution Medium
A.
B.
C.
D.

25 Calls arrive at a help desk according to a Poisson distribution with a mean of calls per hour. What is the probability of receiving exactly calls in the next hour?

Poisson distribution Medium
A.
B.
C.
D.

26 A basketball player makes a free throw with probability . If she takes independent free throws, what is the probability that she makes exactly ?

binomial distribution Medium
A.
B.
C.
D. , obtained by multiplying only the success probabilities

27 The mean of observations is . If an observation equal to is replaced by , what is the new mean?

mean Medium
A.
B.
C.
D.

28 The ordered data set is . A number is added, and the median of the resulting seven values is . What must be?

median Medium
A.
B. , since it was the upper middle value before insertion
C.
D.

29 The values have frequencies , respectively. If there are observations and is the unique mode, what is ?

mode Medium
A.
B.
C.
D.

30 A random variable has standard deviation . If , what is the standard deviation of ?

standard deviation Medium
A.
B.
C. , after including both the multiplier and the added constant
D.

31 Two cards are drawn without replacement from a standard -card deck. Given that the first card is an ace, what is the probability that the second card is also an ace?

conditional probability Medium
A.
B.
C.
D.

32 A disease affects of a population. A test has sensitivity and a false-positive rate of . If a person tests positive, what is the approximate probability that the person has the disease?

Bayes theorem Medium
A. , because this is the stated sensitivity of the test
B.
C.
D.

33 A random variable takes values , , and with probabilities , , and . What is ?

random variables Medium
A.
B.
C.
D.

34 A continuous random variable is uniformly distributed on and has mean . What is ?

uniform distribution Medium
A.
B.
C.
D.

35 Package weights are normally distributed with mean g and standard deviation g. Using , what weight marks the th percentile?

normal distribution Medium
A. g
B. g
C. g
D. g, after treating the percentile value as a percentage increase

36 The waiting time in hours follows an exponential distribution with rate . What is ?

exponential distribution Medium
A.
B.
C.
D.

37 Printing errors occur at an average rate of per hour according to a Poisson process. What is the probability of at least one error during a -minute period?

Poisson distribution Medium
A.
B.
C.
D.

38 Each manufactured item is defective with probability , independently of the others. What is the probability that at least one of items is defective?

binomial distribution Medium
A.
B.
C. , which represents exactly one defective item
D.

39 For events and , suppose , , and . Which statement is correct?

conditional probability Medium
A. and are independent
B. and are mutually exclusive
C. , so both events have equal probabilities
D.

40 Factory produces of a company's items and has a defect rate of . Factory produces and has a defect rate of . Given that an item is defective, what is the probability it came from factory ?

Bayes theorem Medium
A.
B.
C.
D.

41 The joint density of continuous random variables and is for , and otherwise. What is ?

random variables Hard
A.
B.
C.
D.

42 Let be independent uniform random variables on . Given that , what is the expected sample range?

uniform distribution Hard
A.
B.
C.
D.

43 Let and be independent standard normal variables. Define and . What is ?

normal distribution Hard
A.
B.
C.
D.

44 Let and be independent, where the parameters are rates. What is ?

exponential distribution Hard
A.
B.
C.
D.

45 Let and be independent. For a positive integer , what is ?

Poisson distribution Hard
A.
B.
C.
D.

46 If , what is ?

binomial distribution Hard
A.
B.
C.
D.

47 A nonnegative integer-valued random variable satisfies for every integer . What is ?

mean Hard
A.
B.
C.
D.

48 A continuous random variable has density for , and otherwise. What is its unique median?

median Hard
A.
B.
C.
D.

49 Let and define . What is the unique mode of ?

mode Hard
A.
B.
C.
D.

50 Group A has observations with mean and population standard deviation . Group B has observations with mean and population standard deviation . What is the population standard deviation of the combined group?

standard deviation Hard
A.
B.
C.
D.

51 Two cards are drawn uniformly without replacement from a standard -card deck. Given that at least one card is an ace, what is the probability that both cards are aces?

conditional probability Hard
A.
B.
C.
D.

52 A disease has prevalence . Two tests are conditionally independent given disease status. Their sensitivities are and , and their specificities are and , respectively. Given that exactly one test is positive, what is the probability of disease?

Bayes theorem Hard
A.
B.
C.
D.

53 Suppose , , and . What is ?

random variables Hard
A.
B.
C.
D.

54 Let and be independent uniform random variables on . What is ?

uniform distribution Hard
A.
B.
C.
D.

55 Let and be independent standard normal variables. What is ?

normal distribution Hard
A.
B.
C.
D.

56 Let and be independent. What is ?

exponential distribution Hard
A.
B.
C.
D.

57 Let . Each of the events is independently accepted with probability . If is the number accepted, what is ?

Poisson distribution Hard
A.
B.
C.
D.

58 A binomial random variable satisfies and . What is ?

binomial distribution Hard
A.
B.
C.
D.

59 Three components operate independently with probabilities , , and , respectively. Given that exactly two components operate, what is the probability that operates?

conditional probability Hard
A.
B.
C.
D.

60 One of two coins is selected with equal prior probability. Coin I has head probability , while Coin II has head probability . The first head occurs on the third toss. What is the posterior probability that Coin II was selected?

Bayes theorem Hard
A.
B.
C.
D.
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