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Compute the expectation of X.
o 7/72
o 1/8
· 5/3
o 4/3
o 23/12
58. A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss?
o 0
o 1/16
o 1/8
· 1/2
o 1/4
59. A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased?
o 1
o 3
· 9
o 27
o 62
60. A random variable Y has the following distribution:
Y | -1 0 1 2
P(Y)| 3C 2C 0.4 0.1 The value of the constant C is:
· 0.1
o 0.15
o 0.20
o 0.25
o 0.75
61. A random variable X has a probability distribution as follows:
X | 0 1 2 3
P(X) | 2k 3k 13k 2k
Then the probability that P(X < 2.0) is equal to
o 0.90
· 0.25
o 0.65
o 0.15
o 1
62. Which one of these variables is a continuous random variable?
· The time it takes a randomly selected student to complete an exam.
o The number of tattoos a randomly selected person has.
o The number of women taller than 68 inches in a random sample of 5 women.
o The number of correct guesses on a multiple choice test.
o The number of 1’s in N rolls of a fair die
63. Heights of college women have a distribution that can be approximated by a normal curve with a mean of 65 inches and a standard deviation equal to 3 inches. About what proportion of college women are between 65 and 67 inches tall?
o 0.75
o 0.5
· 0.25
o 0.17
o 0.85
64. The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What is the "expected value" of the number of patients who are successfully treated?
o 40
o 20
o 8
· 32
o 124
65. A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one of them will be successfully cured?
o 0.5
o 0.36
o 0.2
· 0.04
o 0.4
66. A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as...
· Probability distribution
o The expected value
o The standard deviation
o Coefficient of variation
o Correlation
67. Given a normal distribution with µ=100 and σ=10, what is the probability that X>75?
· 0.99
o 0.25
o 0.49
o 0.45
o 0
68. Which of the following is not a property of a binomial experiment?
o the experiment consists of a sequence of n identical trials
o each outcome can be referred to as a success or a failure
· the probabilities of the two outcomes can change from one trial to the next
o the trials are independent
o binomial random variable can be approximated by the Poisson
69. For a continuous random variable X, the probability density function f(x) represents
o the probability at a fixed value of X
· the area under the curve at X
o the area under the curve to the right of X
o the height of the function at X
o the integral of the cumulative distribution function
70. Two events each have probability 0.2 of occurring and are independent. The probability that neither occur is
· 0.64
o 0.04
o 0.2
o 0.4
o none of the given answers
71. A smoke-detector system consists of two parts A and B. If smoke occurs then the item A detects it with probability 0.95, the item B detects it with probability 0.98 whereas both of them detect it with probability 0.94. What is the probability that the smoke will not be detected?
· 0.01
o 0.99
o 0.04
o 0.96
o None of the given answers
72. A class consists of 490 female and 510 male students. The students are divided according to their marks Passed and Did not pass
| Passed | Did not pass | |
| Female | ||
| Male |
If one person is selected randomly, what is the probability that it did not pass given that it is female.
o 0.06
· 0.12
o 0.41
o 0.81
o 0.19
73. A company which produces a particular drug has two factories, A and B. 30% of the drug are made in factory A, 70% in factory B. Suppose that 95% of the drugs produced by the factory A meet specifications while only 75% of the drugs produced by the factory B meet specifications. If I buy the drug, what is the probability that it meets specifications?
o 0.95
· 0.889
o 0.75
o 0.7
o 0.995
74. Twelve items are independently sampled from a production line. If the probability any given item is defective is 0.1, the probability of at most two defectives in the sample is closest to …
o 0.3874
o 0.9872
o 0.7361
· 0.8891
o None of the shown answers
75. A student can solve 6 from a list of 10 problems. For an exam 8 questions are selected at random from the list. What is the probability that the student will solve exactly five problems?
o 0.98
o 0.02
o 0.28
· 0.53
o None of the shown answers
76. Suppose that 10% of people are left handed. If 8 people are selected at random, what is the probability that exactly 2 of them are left handed?
o 0.0331
o 0.0053
· 0.1488
o 0.0100
o 0.2976
77. Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail presale testing. If you test 4 chips, what is the probability that not all of the chips fail?
· 0.9995
o 5.06 Ч 10-4
o 0.15
o 0.6
o 0.5220
78. Which of these has a Geometric model?
o the number of aces in a five-card Poker hand
o the number of people we survey until we find two people who have taken Statistics
o the number of people in a class of 25 who have taken Statistics
· the number of people we survey until we find someone who has taken Statistics
o the number of sodas students drink per day
79. In a certain town, 50% of the households own a cellular phone, 40% own a pager, and 20% own both a cellular phone and a pager. The proportion of households that own neither a cellular phone nor a pager is
o 90%
o 70%
o 10%
· 30%.
o 25%
80. Four persons are to be selected from a group of 12 people, 7 of whom are women. What is the probability that the first and third selected are women?
· 0.3182
o 0.5817
o 0.78
o 0.916
o 0.1211
81. Twenty percent of the paintings in a gallery are not originals. A collector buys a painting. He has probability 0.10 of buying a fake for an original but never rejects an original as a fake, What is the (conditional) probability the painting he purchases is an original?
o 1/41
· 40/41
o 80/41
o 1
o 40/100
82. Suppose that the random variable T has the following probability distribution:
t | 0 1 2 --------------------------- P(T = t) |.5.3.2
Find 
.
o 0.8
· 0.5
o 0.3
o 0.2
o 0.1
83. A probability function is a rule of correspondence or equation that:
o Finds the mean value of the random variable.
o Assigns values of x to the events of a probability experiment.
· Assigns probablities to the various values of x.
o Defines the variability in the experiment.
o None of the given answers is correct.
84. Which of the following is an example of a discrete random variable?
o The distance you can drive in a car with a full tank of gas.
o The weight of a package at the post office.
o The amount of rain that falls over a 24-hour period.
· The number of cows on a cattle ranch.
o The time that a train arrives at a specified stop.
85. Which of the following is the appropriate definition for the union of two events A and B?
o The set of all possible outcomes.
o The set of all basic outcomes contained within both A and B.
· The set of all basic outcomes in either A or B, or both.
o None of the given answers
o The set of all basic outcomes that are not in A and B.
86. Johnson taught a music class for 25 students under the age of ten. He randomly chose one of them. What was the probability that the student was under twelve?
· 1
o 0.5
o 1/25
o 0
o 0.25
87. The compact disk Jane bought had 12 songs. The first four were rock music. Tracks number 5 through 12 were ballads. She selected the random function in her CD Player. What is the probability of first listening to a ballad?
o 1/3
· 2/3
o 1/2
o 1/6
o 1/12
88. Two fair dice, one red and one blue, each have numbers 1-6. If a roll of the two dice totals 6, what is the probability that the red die is showing a 5?
o 1/6
· 1/5
o 1/3
o 5/6
o 1/18
89. A regular deck of 52 cards contains 4 different suits (Spades, Hearts, Diamonds, and Clubs) that each have 13 cards. If you randomly choose two cards from the deck, what is the probability that both cards will all be hearts?
o 4/17
· 1/17
o 2/17
o 1/4
o 4/17
o 33/68
90. What is the probability of drawing a diamond from a standard deck of 52 cards?
o 1/52
o 13/39
o 1/13
· 1/4
o 1/2
91. One card is randomly selected from a shuffled deck of 52 cards and then a die is rolled. Find the probability of obtaining an Ace and rolling an odd number.
o 1/104
o 7/13
o 1/39
· 1/26
o 1/36
92. The probability that a particular machine breaks down on any day is 0.2 and is independent of the breakdowns on any other day. The machine can break down only once per day. Calculate the probability that the machine breaks down two or more times in ten days.
o 0.0175
o 0.0400
o 0.2684
· 0.6242
o 0.9596
93. Let A, B and C be independent events such that P(A) = 0.5, P(B) = 0.6 and P(C) = 0.1. Calculate 
o 0.69
o 0.71
· 0.73
o 0.98
o 1
94. The pdf of a random variable X is given by 
.
What are the values of µ and σ?
o 
o 
· 
o 
o 
95. What quantity is given by the formula 
?
o Covariance of the random variables X and Y
· Correlation coefficient
o Coefficient of symmetry
o Conditional expectation
o None of the given answers is correct
96. In the first step, Joe draws a hand of 5 cards from a deck of 52 cards. What is the probability that Joe has exactly one ace? oersons A and B Напишите здесь вопрос с множественным выбором
· 0.2995
o 0.699
o 0.23336
o 1/4
o 0.4999
97. The number of clients arriving each hour at a given branch of a bank asking for a given service follows a Poisson distribution with parameter λ=3. It is assumed that arrivals at different hours are independent from each other. The probability that in a given hour at most 2 clients arrive at this specific branch of the bank is:
o 0.64726
o 0.81521
· 0.42319
o 0.18478
o 0.08391
98. Table shows the cumulative distribution function of a random variable X. Determine 
.
| X | ||||
| F(X) | 1/8 | 3/8 | 3/4 |
o 1/8
· 7/8
o 1/2
o 3/4
o 1/3
99. Table shows the cumulative distribution function of a random variable X. Determine 
.
| X | ||||
| F(X) | 1/8 | 3/8 | 3/4 |
o 1/8
o 1
o 1/2
o 3/4
· 0
100. Which of the following statements is always true for A and 
?
o P(AAc)=1
o P(Ac)=P(A)
o P(A+Ac)=0
· P(AAc)=0
o None of the given statements is true
101. Consider the universal set U and two events A and B such that 
and 
. We know that P(A)=1/3. Find P(B).
· 2/3
o 1/3
o 4/9
o Cannot be determined
o 1
102. A box contains 5 red and 4 white marbles. Two marbles are drawn successively from the box without replacement and it is noted that the second one is white. What is the probability that the first is also white?
o 1/3
· 3/8
o 5/8
o 1/8
o 1
103. If P(A)=1/2 and P(B)=1/2 then 
o 1/4, always
· 1/4, if A and B are independent
o 1/2, always
o 1/2, if A and B are independent
o None of the given answers
104. Suppose that P(A|B)=3/5, P(B)=2/7, and P(A)=1/4. Determine P(B|A).
o 24/75
· 24/35
o 6/35
o 12/75
o None of the given answers
105. A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and without replacement. Calculate the probability that the number of boys selected exceeds the number of girls selected.
o 512/3375
· 28/65
o 8/15
o 1856/3375
o 36/65
106. If the variance of a random variable X is equal to 3, then Var(2X) is:
· 12
o 6
o 3
o 1
o 9
107. Let X and Y be continuous random variables with joint cumulative distribution function 
for 
and 
. Find P(X>2).
o 3/125
o 11/50
· 12/25
o 
o 
108. Indicate the correct statement related to Poisson random variable 
.
· 
, 
o 
, 
o 
, 
o 
, 
is const
o None of the given answers is correct
109. Напишите здесь вопрос с множественным выбором
o 0.16
· 0.08
o 0.31
o 0.38
o 0.46
o o ui
110. We are given the pmf of two random variables X and Y shown in the tables below.
| Х | У | ||||||
| px | 0,4 | 0,6 | py | 0,2 | 0,8 |
Find E[X+Y].
· 5,8
o 2,2
o 2
o 8,8
o 10
111. The pdf of a random variable X is given by 
. Calculate the parameter 
.
o 0
· 4
o 1,5
o 2
o 3,5
112. Four persons are to be selected from a group of 12 people, 7 of whom are women. What is the probability that three of those selected are women?
· 0.35
o 0.65
o 0.45
o 0.25
o 0.1211
113. Suppose that the random variable T has the following probability distribution:
t | 0 1 2 --------------------------- P(T = t) |.5.3.2 Find 
.
· 0.8
o 0.5
o 0.3
o 0.2
o 0.1
114. Suppose that the random variable T has the following probability distribution:
t | 0 1 2 --------------------------- P(T = t) |.5.3.2 Compute the mean of the random variable T.
o 0.8
o 0.5
· 0.7
o 0.1
o 1
115. Three dice are rolled. What is the probability that the points appeared are distinct.
o 1
· 5/9
o 2
o 1/3
o 1/2
116. Probability density function of the normal random variable X is given by 
. What is the standard deviation?
· 5
o 3
o 25
o 50
o 9
117. The event A occurs in each of the independent trials with probability p. Find probability that event A occurs at least once in the 5 trials.
o 
· 
o 
o 
o None of the given answers is correct
118. The cdf of a random variable X is given by 
Find the probability P(1.7<X<1.9).
o 0,16
o 0,8
o 1
· 0,4
o 0.6
119. In each of the 20 independent trials the probability of success is 0.2. Find the variance of the number of successes in these trials.
o 0
o 1
o 10
· 3.2
o 0.32
120. A coin tossed twice. What is the probability that head appears in the both tosses.
o 1/2
· 1/4
o 0
o 4:1
o 1
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