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The probabilities that three men hit a target are respectively 1/6, 1/4 and 1/3. Each man shoots once at the target. What is the probability that exactly one of them hits the target?
11/72
21/72
31/72
3/4
17/72
A problem in mathematics is given to three students whose chances of solving it are 1/3, 1/4, 1/5. What is the probability that the problem will be solved?
0.2
0.8
0.4
0.6
1
You are given P[A∪B] = 0.7 and P[A∪Bc] = 0.9 . Determine P[A] .
0.2
0.3
0.4
0.6
0.8
An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44 . Calculate the number of blue balls in the second urn.
4
20
24
44
64
The probability that a boy will not pass an examination is 3/5 and that a girl will not pass is 4/5. Calculate the probability that at least one of them passes the examination.
11/25
13/25
1/2
7/25
16/25
A bag contains 5 red discs and 4 blue discs. If 3 discs are drawn from the bag without replacement, find the probability that all three are blue.
1/21
2/21
1/7
4/21
1/3
Find the variance for the given probability distribution.
|
X |
0 |
2 |
4 |
6 |
|
P(x) |
0.05 |
0.17 |
0.43 |
0.35 |
1.5636
2.8544
1.6942
2.4484
1.7222
A bag contains 5 white, 7 red and 8 black balls. Four balls are drawn one by one with replacement, what is the probability that at least one is white?
0.7182
Формулой Бернулли называется формула
Indicate the formula of computing variance of a random variable X with expectation µ.
How would it change the variance of a random variable X if we add a number to the X?
Var(X+a)=Var(X)+a
Var(X+a)=Var(X)+a2
Var(X+a)=Var(X)
Var(X+a)=Var(X)
Var(X+a)=Var(X)+a2
How would it change the expected value of a random variable X if we multiply the X by a number k.
Which of the following expressions indicates the occurrence of exactly one of the events A, B, C?
Which of the following expressions indicates the occurrence of at least one of the events A, B, C?
Which of the following expressions indicates the occurrence of all three events A, B, C simultaneously?
Which of the following expressions indicates the occurrence of exactly two of events A, B, C?
Conditional probability P(A|B) can be defined by
Urn I contains a white and b black balls, whereas urn II contains c white and d black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be both black?
The table below shows the probability mass function of a random variable X.
|
xi |
0 |
x2 |
5 |
|
pi |
0.1 |
0.2 |
0.7 |
If E[X]=5,5 find the value of x2.
3
1
12
0.8
10
The probability of machine failure in one working day is equal to 0.01. What is the probability that the machine will work without failure for 5 days in a row.
0.99999
0.95099
1
0.05
0.55
The cumulative distribution function of a discrete random variable X is given by Find P{3<X<9}.
0,4
0,5
0,6
0,9
1
A fair die is rolled three times. A random variable X denotes the number of occurrences of 6’s. What is the probability that X will have the value which is not equal to 0.
91/216
125/216
25/216
1/216
215/216
Find the expectation of a random variable X if the cdf .
-5
e-5
5
6
1/5
Compute the mean for continuous random variable X with probability density function .
2/3
0
1/3
1
Mean does not exist
If the variance of a random variable X is given Var(X)=3. Then Var(2X) is
12
6
3
1
9
Indicate the expectation of a Poisson random variable X with parameter .
0
Indicate the variance of a Poisson random variable X with parameter .
0
Indicate the formula for conditional expectation.
The table below shows the pmf of a random variable X. What is the Var(X)?
|
X |
-2 |
1 |
2 |
|
Р |
0,1 |
0,6 |
0,3 |
0.5
1.67
4.71
1.2
4.7
The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 6.
0.04
0.15
0.47
0.53
0.94
The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 5.
0.03
0.13
0.42
0.58
0.97
If Var(X)=2, find Var(-3X+4).
12
10
9
18
3
The table below shows the pmf of a random variable X. Find E[X] and Var(X).
|
X |
-1 |
0 |
1 |
|
P |
0.2 |
0.3 |
0.5 |
E[X]= 0,7; Var(X) =0.24
E[X]= 0,3; Var(X) =0.27
E[X]= 0,3; Var(X) =0.61
E[X]= 0,8; Var(X) =0.21
E[X]= 0,8; Var(X) =0.24
What kind of distribution is given by the density function ()?
Poisson distribution
Normal distribution
Uniform distribution
Bernoulli distribution
Exponential distribution
If a fair die is tossed twice, the probability that the first toss will be a number less than 4 and the second toss will be greater than 4 is
1/3
5/6
1/6
3/4
0
A class consists of 490 female and 510 male students. The students are divided according to their marks
|
|
Passed |
Did not pass |
|
Female |
430 |
60 |
|
Male |
410 |
100 |
If one person is selected randomly, the probability that it did not pass given that it is female is:
0.06
0.12
0.41
0.81
none of the shown answers
Marks on a Chemistry test follow a normal distribution with a mean of 65 and a standard deviation of 12. Approximately what percentage of the students have scores below 50?
11%
89%
15%
18%
39%
Suppose the test scores of 600 students are normally distributed with a mean of 76 and standard deviation of 8. The number of students scoring between 70 and 82 is:
272
164
260
136
328
The distribution of weights in a large group is approximately normally distributed. The mean is 80 kg. and approximately 68% of the weights are between 70 and 90 kg. The standard deviation of the distribution of weights is equal to:
20
5
40
50
10
The probability density function of a continuous random variable X is
. Find .
0.5625
0.3125
0.1250
0.4375
0.1275
Let X be a continuous random variable with density function Calculate the expected value of X.
1/5
3/5
1
28/15
12/5
The probability density function of a continuous random variable X is . Find the value of k.
2
0.25
0.375
2.25
Any positive value greater than 2
A continuous random variable X is uniformly distributed over the interval [10, 16]. The expected value of X is
16
13
10
7
6
If X and Y are independent random variables with , , and , , , . Then is
0.30
0.56
0.70
0.80
1
How many different three-member teams can be formed from six students?
20
120
216
720
6
How many different 6-letter arrangements can be formed using the letters in the word ABSENT, if each letter is used only once?
6
36
720
46.656
72
If P(E) is the probability that an event will occur, which of the followings must be false?
P(E)=1
P(E)=1/2
P(E)=1/3
P(E)= -1
P(E)=0
A die is rolled. What is the probability that the number rolled is greater than 2 and even?
1/2
1/3
2/3
5/6
0
A pair of dice is rolled. A possible event is rolling a multiple of 5. What is the probability of the complement of this event?
2/36
12/36
29/36
32/36
9/36
The cumulative distribution function for continuous random variable X is given by . Find the standard deviation .
A continuous random variable X uniformly distributed on [-2;6]. Find E[X] and Var(X).
4 and
and 2
2 and
and 2
2 and
A continuous random variable X is exponentially distributed with the density . What is the E[X] and Var(X)?
and
and
and
and
and
The expression is equivalent to
Evaluate 1!+2!+3!
5
6
9
10
12
A pair of dice is rolled. A possible event is rolling a multiple of 5. What is the probability of the complement of this event?
2/36
12/36
29/36
32/36
1/36
Your state issues license plates consisting of letters and numbers. There are 26 letters and the letters may be repeated. There are 10 digits and the digits may be repeated. How many possible license plates can be issued with two letters followed by three numbers?
25000
67600
250000
676000
2500
A random variable X has the cumulative distribution function
Compute the expectation of X.
7/72
1/8
5/6
4/3
23/12
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?
0
1/16
1/8
1/2
1/4
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?
1
3
9
27
62
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
0.15
0.20
0.25
0.75
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
0.90
0.25
0.65
0.15
1
Which one of these variables is a continuous random variable?
The time it takes a randomly selected student to complete an exam.
The number of tattoos a randomly selected person has.
The number of women taller than 68 inches in a random sample of 5 women.
The number of correct guesses on a multiple choice test.
The number of 1’s in N rolls of a fair die
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?
0.75
0.5
0.25
0.17
0.85
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?
40
20
8
32
124
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?
0.5
0.36
0.2
0.04
0.4
A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as ...
Probability distribution
The expected value
The standard deviation
Coefficient of variation
Correlation
Given a normal distribution with µ=100 and σ=10, what is the probability that X>75?
0.99
0.25
0.49
0.45
0
Which of the following is not a property of a binomial experiment?
the experiment consists of a sequence of n identical trials
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
the trials are independent
binomial random variable can be approximated by the Poisson
Which of the following random variables would you expect to be discrete?
The weights of mechanically produced items
The number of children at a birthday party
The lifetimes of electronic devices
The length of time between emergency arrivals at a hospital
The times, in seconds, for a 100m sprint
Two events each have probability 0.2 of occurring and are independent. The probability that neither occur is
0.64
0.04
0.2
0.4
none of the given answers
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
0.99
0.04
0.96
None of the given answers
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 |
430 |
60 |
|
Male |
410 |
100 |
If one person is selected randomly, what is the probability that it did not pass given that it is male.
0.066
0.124
0.414
0.812
0.196
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?
0.95
0.81
0.75
0.7
0.995
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 …
0.3874
0.9872
0.7361
0.8891
None of the shown answers
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?
0.282
0.02
0.376
0.133
None of the shown answers
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?
0.0331
0.0053
0.1488
0.0100
0.2976
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
5.06 × 10-4
0.15
0.6
0.5220
Which of these has a Geometric model?
the number of aces in a five-card Poker hand
the number of people we survey until we find two people who have taken Statistics
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
the number of sodas students drink per day
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
90%
70%
10%
30%.
25%
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
0.5817
0.78
0.916
0.1211
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?
1/41
40/41
80/41
1
40/100
Suppose that the random variable T has the following probability distribution:
t | 0 1 2 --------------------------- P(T = t) | .5 .3 .2
Find .
0.8
0.5
0.3
0.2
0.1
A probability function is a rule of correspondence or equation that:
Finds the mean value of the random variable.
Assigns values of x to the events of a probability experiment.
Assigns probablities to the various values of x.
Defines the variability in the experiment.
None of the given answers is correct.
Which of the following is an example of a discrete random variable?
The distance you can drive in a car with a full tank of gas.
The weight of a package at the post office.
The amount of rain that falls over a 24-hour period.
The number of cows on a cattle ranch.
The time that a train arrives at a specified stop.
Which of the following is the appropriate definition for the union of two events A and B?
The set of all possible outcomes.
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.
None of the given answers
The set of all basic outcomes that are not in A and B.
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
0.5
1/25
0
0.25
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?
1/3
2/3
1/2
1/6
1/12
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?
1/6
1/5
1/3
5/6
1/18
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?
4/17
1/17
2/17
1/4
4/17
33/68
What is the probability of drawing a diamond from a standard deck of 52 cards?
1/52
13/39
1/13
1/4
1/2
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.
1/104
7/13
1/39
1/26
1/36
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.
0.0175
0.0400
0.2684
0.6242
0.9596
Let A, B and C be independent events such that P(A) = 0.5, P(B) = 0.6 and P(C) = 0.1. Calculate
0.69
0.71
0.73
0.98
1
The pdf of a random variable X is given by.
What are the values of µ and σ?
What quantity is given by the formula ?
Covariance of the random variables X and Y
Correlation coefficient
Coefficient of symmetry
Conditional expectation
None of the given answers is correct
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?
0.2995
0.699
0.23336
1/4
0.4999
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:
0.64726
0.81521
0.42319
0.18478
0.08391
Table shows the cumulative distribution function of a random variable X. Determine .
|
X |
1 |
2 |
3 |
4 |
|
F(X) |
1/8 |
3/8 |
3/4 |
1 |
1/8
7/8
1/2
3/4
1/3
Table shows the cumulative distribution function of a random variable X. Determine .
|
X |
1 |
2 |
3 |
4 |
|
F(X) |
1/8 |
3/8 |
3/4 |
1 |
1/8
1
1/2
3/4
0
Which of the following statements is always true for A and ?
P(AAc)=1
P(Ac)=P(A)
P(A+Ac)=0
P(AAc)=0
None of the given statements is true
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
1/3
4/9
Cannot be determined
1
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?
1/3
3/8
5/8
1/8
1
If P(A)=1/2 and P(B)=1/2 then
1/4, always
1/4, if A and B are independent
1/2, always
1/2, if A and B are independent
None of the given answers
Suppose that P(A|B)=3/5, P(B)=2/7, and P(A)=1/4. Determine P(B|A).
24/75
24/35
6/35
12/75
None of the given answers
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.
512/3375
28/65
8/15
1856/3375
36/65
If the variance of a random variable X is equal to 3, then Var(3X) is :
12
6
3
27
9
Let X and Y be continuous random variables with joint cumulative distribution function for and . Find P(X>2).
3/125
11/50
12/25
Indicate the correct statement related to Poisson random variable .
,
,
,
, is const
None of the given answers is correct
Let X be a continuous random variable with PDF f(x) = cx (0 ≤ x ≤ 1), where c is a constant. Find the value of constant c.
1
2
1/2
3/2
4
We are given the pmf of two random variables X and Y shown in the tables below.
|
Х |
1 |
3 |
У |
2 |
4 |
||
|
px |
0,4 |
0,6 |
py |
0,2 |
0,8 |
Find E[X+Y].
5,8
2,2
2
8,8
10
The pdf of a random variable X is given by . Calculate the parameter .
0
4
1,5
2
3,5
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
0.65
0.45
0.25
0.1211
Suppose that the random variable T has the following probability distribution:
t | 0 1 2 --------------------------- P(T = t) | .5 .3 .2 Find .
0.8
0.5
0.3
0.2
0.1
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.
0.8
0.5
0.7
0.1
1
Three dice are rolled. What is the probability that the points appeared are distinct.
1
5/9
2
1/3
1/2
Probability density function of the normal random variable X is given by . What is the standard deviation?
5
3
25
50
9
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.
None of the given answers is correct
The cdf of a random variable X is given by Find the probability P(1.7<X<1.9).
0,16
0,8
1
0,4
0.6
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.
0
1
10
3.2
0.32
A coin tossed twice. What is the probability that head appears in the both tosses.
1/2
1/4
0
4:1
1
Continuous random variable X is normally distributed with mean=1 and variance=4. Find P(4≤x≤6).
0,0606
0,202
0,0305
0,0484
0,0822
Random variable X is uniformly distributed on the interval [-2, 2]. Indicate the right values for E[X] and Var(X).
E[X]=0 and Var(X)=4
E[X]=0 and Var(X)=1.33
E[X]=0.5 and Var(X)=1.33
E[X]=0 and Var(X)=0
No right answer
Expectation and standard deviation of the normally distributed random variable X are respectively equal to 15 and 5. What is the probability that in the result of an experiment X takes on the value in interval (5, 20)?
(20) – (5)
(5) + (10)
(1) – (0)
(20) + (5)
(1) + (2)-1
(2) – (1)
Normally distributed random variable X is given by density . Find the mean.
-1/2
1/2
1/4
0
1
Indicate the density function of the normally distributed random variable X when mean=2 and variance=9.
Indicate the PDF for standard normal random variable.
,
,
,
Random variable X is uniformly distributed in interval [0, 3]. What is the variance of X?
0.75
1.5
3
0.25
1
Random variable X is uniformly distributed in interval [0, 15]. What is the expectation of X?
15
3.75
7.5
30
0
Random variable X is uniformly distributed in interval [-2, 1]. What is the distribution of the random variable Y=2X+2?
Y is normally distributed in the interval [-4, 2]
Y is uniformly distributed in the interval [-2, 4]
Y is normally distributed in the interval [-2, 4]
Y is exponentially distributed in the interval [-4, 2]
Y has other type of distribution
Random variable X is uniformly distributed in interval [-11, 26]. What is the probability P(X> - 4)?
29/38
29/37
30/37
15/19
0
Random variable X is uniformly distributed in interval [1, 3]. What is the distribution of the random variable Y=3X+1?
Y is normally distributed in the interval [3, 9]
Y is uniformly distributed in the interval [4, 10]
Y is normally distributed in the interval [4, 10]
Y is exponentially distributed in the interval [4, 10]
Y has other type of distribution
Random variable X is uniformly distributed in interval [-11, 20]. What is the probability P(X ≤ 0) ?
11/32
5/16
10/31
11/31
0
Random variable X is given by density function f(x) in the interval (0, 1) and otherwise is 0. What is the expectation of X?
E[X]=0
Random variable X is given by density function f(x) = x/2 in the interval (0, 2) and otherwise is 0. What is the expectation of X?
1/2
1
4/3
2/3
0
Random variable X is given by density function f(x) = 2x in the interval (0, 1) and otherwise is 0. What is the expectation of X?
1/2
1
4/3
2/3
0
Random variable X is given by density function f(x) = 2x in the interval (0, 1) and otherwise is 0. What is the probability P(0 < X < 1/2) ?
1/2
1/4
0
1/8
0
None of these
Indicate the function that can be CDF of some random variable.
None of these
Indicate the function that can be PDF of some random variable.
Continuous random variable X has the following CDF:
. What is the PDF of X in the interval 1<X≤2?
1/2
0
1
X2/4
x
Continuous random variable X is given in the interval [0, 100]. What is the probability P(X=50)?
0
1
0.5
0.75
0.25
CDF of discrete random variable X is given by
What is the probability P{1.3<X≤2.3}?
0.8
0.2
0
0.6
0.4
PMF of discrete random variable is given by
|
Х |
0 |
2 |
4 |
|
Р |
0,1 |
0,5 |
0,4 |
Find the value of CDF of X in the interval (2, 4].
0.4
0.5
0.2
0.6
1
PMF of discrete random variable is given by
|
Х |
0 |
2 |
4 |
|
Р |
0,3 |
0,1 |
0,6 |
Find F(2).
0.4
0.6
0.3
0.7
0.1
PMF of discrete random variable X is given by
|
Х |
-1 |
5 |
|
Р |
0,4 |
0,6 |
Find standard deviation of X.
15.4
8.64
2.6
2.9393
3.3333
PMF of discrete random variable X is given by
|
Х |
-1 |
5 |
|
Р |
0,4 |
0,6 |
Find variance of X.
15.4
8.64
2.6
2.93
3.33
PMF of discrete random variable X is given by
|
Х |
0 |
5 |
|
|
Р |
0,6 |
0,1 |
0,3 |
If E[X]=3.5 then find the value of x3.
10
6
8
12
24
Probability of success in each of 100 independent trials is constant and equals to 0.8. What is the probability that the number of successes is between 60 and 88?
A man is made 10 shots on the target. Assume that the probability of hitting the target in one shot is 0,7. What is the most probable number of hits?
8
7
6
5
9
Consider two boxes, one containing 4 white and 6 black balls and the other - 8 white and 2 black balls. A box is selected at random, and a ball is drawn at random from the selected box. If the ball occurs to be white, what is the probability that the first box was selected?
0.4
0.6
0.8
1/3
2/3
Each of two boxes contains 6 white and 4 black balls. A ball is drawn from 1st box and it is replaced to the 2nd box. Then a ball is drawn from the 2nd box. What is the probability that this ball occurs to be white?
0.3
0.4
0.5
0.6
0.8
Consider two boxes, one containing 3 white and 7 black balls and the other – 1 white and 9 black balls. A box is selected at random, and a ball is drawn at random from the selected box. What is the probability that the ball selected is black?
0.8
0.2
0.4
1.6
0.9
Urn I contains 4 black and 6 white balls, whereas urn II contains 3 white and 7 black balls. An urn is selected at random and a ball is drawn at random from the selected urn. What is the probability that the ball is white?
0.45
0.15
0.4
0.9
1
A coin is tossed twice. Event A={ at least one Head appears}, event B={at least one Tail appears}. Find the conditional probability P(B|A).
2/3
1/3
1/2
3/4
0
A coin is tossed twice. Event A={ Head appears in the first tossing}, event B={at least one Tail appears}. Find the conditional probability P(B|A).
1/4
1/2
1/3
2/3
3/4
Probability that each shot hits a target is 0.9. Total number of shots produced to the target is 5. What is the probability that at least one shot hits the target?
1-0,95
0,95
1-50,9
1-0,15
0,15
1-50,1
An urn contains 1 white and 9 black balls. Three balls are drawn from the urn without replacement. What is the probability that at least one of the balls is white?
0.7
0.3
0.4
0.2
0.6
Four independent shots are made to the target. Probability of missing in the first shot is 0.5; in the second shot – 0.3; in the 3rd – 0.2; in the 4th – 0.1. What is the probability that the target is not hit.
1.1
0.03
0.275
0.003
1.01
Probability of successful result in the certain experiment is 3/4. Find the most probable number of successful trials, if their total number is 10.
6
7
8
5
10
Let E and F be two mutually exclusive events and P(E)=P(F)=1/3. The probability that none of them will occur is:
No correct answer
Let E and F be two events. If , , and , then the conditional probability of E given F is:
No correct answer
Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?
1.8
1.54
2.1
1.77
3
At a university, 14% of students take math and computer classes, and 67% take math class. What is the probability that a student takes computer class given that the student takes math class?
0.81
0.21
0.53
No correct answer
0.96
Let , , , be the joint p.d.f. of X and Y. Find the marginal PDF of X.
x
x+1/2
y+1/2
x2+1
x2+y2
If two random variables X and Y have the joint density function, , find the probability P(X+Y<1).
1/24
1/12
5/12
1/4
0.003
If two random variables X and Y have the joint density function, , find the conditional PDF .
None of these
If two random variables X and Y have the joint density function, , find the conditional PDF .
None of these
A basketball player makes 90% of her free throws. What is the probability that she will miss for the first time on the seventh shot?
0.0001
0.053
0.002
0.001
0.01
The joint distribution for two random variables X and Y is given by . Then find P(Y>0.5).
0.5
0.25
0.75
1
1.5
Let X be a continuous random variable with probability density given by . Let Y=2X-3. Find P(Y≥4).
0.3438
0.53125
0.0625
0.1563
0
Random variable X has the following PDF
Find .
0.31
0.428
0.512
0
0.78
Random variable X has the following PDF
Find E[X].
0
1
2
3
4
Random variable X has the following PDF
Find Var[X].
0
1
0.6
0.8
0.4
Random variable X has the following PDF
Find .
4
0
2
1
-2
The joint distribution for two random variables X and Y is given by . Find the marginal density function for X.
6y
6y2
6x2
3x2
3x3
The joint distribution for two random variables X and Y is given by . Find the marginal density function for Y.
3x2
6y
2y
2y2-1
y+6
The joint distribution for two random variables X and Y is given by . Find the E[X].
0.25
0.75
0.5
0.95
None of these
The joint distribution for two random variables X and Y is given by . Find the E[Y].
1
2/3
1/3
0.5
0.25
Assume that Z is standard normal random variable. What is the probability P(|Z|>2.53)?
0.9943
0.0114
0.0057
0.9886
None of these
If Z is normal random variable with parameters µ=0, σ2=1 then the value of c such that P(|Z|<c)=0.7994 is
1.28
0.84
1.65
2.33
None of these
The random variable X has the continuous CDF
. Find P(2≤X≤4).
16/9
4/3
4/9
5/9
2/3
Let X be the random variable for the life in hours for a certain electronic device. The probability density function is
. Find the expected life for a component.
2000 hours
1000 hours
100 hours
200 hours
None of these
The joint distribution for two random variables X and Y is given by . Find E[X-Y].
0
7/6
2/3
1/6
None of these
The joint distribution for two random variables X and Y is given by . Find E[X+Y].
1/6
6/7
7/6
5/6
0
The joint density function for the random variables X and Y is given by . Find E[X].
0
1
1.4142
2
None of these
A box contains 15 balls, 10 of which are black. If 3 balls are drawn randomly from the box, what is the probability that all of them are black?
0.26
0.52
0.1
None of these
0.36
The Cov(aX,bY) is equal to
If A and B are two mutually exclusive events with P(A) = 0.15 and P(B) = 0.4, find the probability P(A and Bc) (i.e. probability of A and B complement).
0.4
0.15
0.85
0.6
0.65
From a group of 5 men and 6 women, how many committees of size 3 are possible with two men and 1 woman if a certain man must be on the committee?
None of these
Let , , , be the joint PDF of X and Y. Find the marginal PDF of Y.
y+1/2
y
1/2y
y2/2
1/2
Let , , , be the joint PDF of X and Y. Compute E[X].
0.2
0.823
0.583
1
0
Let , , , be the joint PDF of X and Y. Compute E[Y].
0.2
0.823
0.583
1
0
Let , , , be the joint PDF of X and Y. Compute E[2X].
7/6
0
1
7/12
1/6
Let X be continuous random variable with probability density function . Find the expected value of random variable X.
19/3
13/3
12/7
28/9
27/4
The joint distribution for two random variables X and Y is given by . Then find P(X>0.5).
0.5
0.25
0.15
0.75
0.1
Probability mass function for discrete random variable X is represented by the
graph. Find Var(X).
1
4
5
2
6
Two dice are rolled, find the probability that the sum is less than 13.
1
1.2
0.5
0.6
0.8
A bag has six red marbles and six blue marbles. If two marbles are drawn randomly from the bag, what is the probability that they will both be red?
1/2
11/12
5/12
5/22
1/3
A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
175/256
1
1/256
81/256
144/256
Let random variable X be normal with parameters mean=5, variance=9. Which of the following is a standard normal variable?
Z=(X-5)/5
Z=(X-3)/5
Z=(X-5)/3
Z=(X-3)/3
None of these
Конец формы
None of these