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1Bob has three bookshelves in his office and 15 books (5 are math books, 10 are novels). If each shelf holds exactly five books and books are placed randomly on the shelves (all orderings are equally likely), how many ways can 15 books be arranged on a bookshelves?
- A15!/10!
- B15!/(15!*10!)
- C15!/(5!)^3
- D15!/(3!)^3
- E15!*3!/(15!*10!)
2A class in probability theory consists of 2 men and 8 women. They passed exam, took their score. Assume that no two students took the same score. How many different scores are possible?
- A2!*8!
- B10!
- C10!/2!
- D10!/(2!*8!)
- E10!/(2!)^2
3A class in probability theory consists of 6 men and 4 women. They passed exam, took their score. Assume that no two students took the same score. How many different scores are possible?
- A6!*4!
- B10!
- C10!/2!
- D10!/(6!*4!)
- E10!/(2!)^2
4Ms. Jones has 10 books that she is going to put on her bookshelf. Of these, 4 are math books, 3 are chemistry books, 2 are history books, and 1 is a language book. Ms. Jones wants to arrange her books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible?
- A288
- B6912
- C12600
- D525
- E3456
5How many different signals, each consisting of 9 flags hung in a line, can be made from a set of 4 white flags, 3 red flags, and 2 blue flags if all flags of the same color are identical?
- A288
- B6912
- C1260
- D525
- E3456
6From a group of 5 women and 7 men, how many different committees consisting of 2 women and 3 men can be formed, if 2 of the men are refuse to serve on the committee together?
- A350
- B300
- C4200
- D500
- E220
7A student answers to 10 questions in an examination. How many choices if she answered at 7 questions?
- A120
- B176
- C45
- D10
- E220
8A student answers to 10 questions in an examination. How many choices if she answered at least 7 questions?
- A120
- B176
- C45
- D10
- E220
9An urn contains 30 balls, of which 10 are red and the other 20 blue. Suppose you take out 8 balls from this urn, without replacement. In how many ways among chosen 8 balls in this sample exactly 3 are red and 5 are blue?
- A5852925
- B1860480
- C3720960
- D2480640
- E4961280
10A bag contains six Scrabble tiles with the letters A-D-M-N-O-R. You reach into the bag and take out tiles one at a time. After you pick a tile from the bag, write down that letter and then return the tile to the bag. How many possible words can be formed?
- A720
- B6
- C46656
- D120
- E10240
11A police department in a small city consists of 10 officers. If the department policy is to have 5 of the officers patrolling the streets, 2 of the officers working full time at the station, and 3 of the officers on reserve at the station, how many different divisions of the 10 officers into the 3 groups are possible?
- A350
- B2520
- C4200
- D300
- E220
12Joel has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Joel's Jumble has 2 classical songs, 13 rock songs and 5 rap songs on it. What is the probability that the selected song is classical song or rap song?
- A0.9
- B13/20
- C0.35
- D7
- E0.7
13A chess tournament has 10 competitors, of which 4 are Russian, 3 are from the USA, 2 are from Great Britain, and 1 is from Brazil. If the tournament result lists just the nationalities of the players in the order in which they placed, how many outcomes are possible?
- A288
- B6912
- C12600
- D525
- E3456
14An 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.
- A64
- B16
- C4
- D32
- E8
15An 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 different color is 0.44. Calculate the number of blue balls in the second urn.
- A4
- B16
- C64
- D32
- E8
16License plates in Minnesota are issued with three letters from A to Z followed by three digits from 0 to 9. If each license plate is equally likely, what is the probability that a random license plate starts with G-Z-N?
- A10^3/26^3
- B10^3
- C1/26^3
- D1/10^3
- E26^3
17A business man has 4 dress shirts and 7 ties. How many different shirt/tie outfits can he create?
- A4
- B7
- C28
- D11
- E8
18Mark is taking four final exams next week. His studying was erratic and all scores A, B, C, D, and F are equally likely for each exam. What is the probability that Mark will get at least one A?
- A0.3264
- B0.8712
- C0.5904
- D0.6124
- E0.9122
19Mark is taking four final exams next week. His studying was erratic and all scores A, B, C, D, and F are equally likely for each exam. What is the probability that Mark will get at least one B?
- A0.3264
- B0.8712
- C0.5904
- D0.6124
- E0.9122
20I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course. Using the given data, answer the following question.
Total number of students 321. What is the probability that a student, taken at random from my class, would have failed the course, given that they failed the final?
- A0.39
- B0.72
- C0.61
- D0.44
- E0.58
21I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course. Using the given data, answer the following question.
Total number of students 321. What is the probability that a student, taken at random from my class, would have passed the course, given that they failed the final?- A0.39
- B0.72
- C0.61
- D0.44
- E0.58
22I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course. Using the given data, answer the following question.
Total number of students 321. What is the probability that a student, taken at random from my class, would have passed the course, given that they passed the final?- A0.39
- B0.72
- C0.81
- D0.44
- E0.61
23I tell students in my class that, although I use an average to calculate their course grades, I do weigh the final exam grade more heavily. I assure them that if they can perform well on my final, then even if they performed poorly on the other exams, they must have learned the material. For three semesters I kept track of how people did on the final and how they did in the course. Using the given data, answer the following question.
Total number of students 321. What is the probability that a student, taken at random from my class, would have failed the course, given that they passed the final?- A0.19
- B0.39
- C0.81
- D0.44
- E0.61
24Insurance predictions for probability of auto accident.
Table gives an insurance company’s prediction for the likelihood that a person in a particular age group will have an auto accident during the next year. The company’s policyholders are 20% under the age of 25, 30% between 25 and 39, and 50% over the age of 40. What is the probability that a random policyholder will have an auto accident next year?
- A0.145
- B0.041
- C0.367
- D0.512
- E0.845
25At a certain university, 4% of men are over 6 feet tall and 1% of women are over 6 feet tall. The total student population is divided in the ratio 3:2 in favour of women (the number of women : the number of men). What is the probability that the randomly selected student is over 6 feet tall?
- A0.05
- B0.022
- C0.14
- D0.028
- E0.11
26You enter a chess tournament where your probability of winning a game is 0.3 against half the players, 0.4 against a quarter of the players, and 0.5 against the remaining quarter of the players. You play a game against a randomly chosen opponent. What is the probability of winning?
- A1.2
- B0.375
- C0.12
- D0.028
- E0.648
27If a person has the disease, the test will detect it with probability 0.95. Also, if the person does not have the disease, the test will report that they do not have it with the same probability 0.95. In addition, it is known from previous data that only 1% of the population has this particular disease. What is the probability that a particular person chosen at random will be tested positive?
- A0,043
- B0,059
- C0,01
- D0,95
- E1,2
28Suppose that you have two bags with white and dark chocolates. Bag 1 has two white chocolates and six dark chocolates. Bag 2 has four white chocolates and two dark chocolates. You choose one bag at random, both being equally likely, and you grab one from the chosen bag. Let A be the event that you grab one white chocolate. Find P(A).
- A11/12
- B11/24
- C13/32
- D1/3
- E1/2
29Amy has two bags of candy. The first bag contains two packs of M&Ms and three packs of Gummi Bears. The second bag contains four packs of M&Ms and two packs of Gummi Bears. Amy chooses a bag uniformly at random and then picks a pack of candy. What is the probability that the pack chosen is Gummi Bears?
- A11/12
- B7/15
- C14/15
- D1/3
- E1/2
30Amy has three bags of candy. The first bag contains one pack of M&Ms and two packs of Gummi Bears. The second bag contains four packs of M&Ms and two packs of Gummi Bears. The third bag contains five packs of M&Ms and three packs of Gummi Bears. Amy chooses a bag uniformly at random and then picks a pack of candy. What is the probability that the pack chosen is M&Ms?
- A11/12
- B13/24
- C2/7
- D5/8
- E1/2
31Amy has two bags of candy. The first bag contains two packs of M&Ms and three packs of Gummi Bears. The second bag contains four packs of M&Ms and two packs of Gummi Bears. Amy chooses the first bag with the probability 0.3 and the second – 0.7. Amy chooses a bag at random and then picks a pack of candy. What is the probability that the pack chosen is M&Ms?
- A13/24
- B44/75
- C7/15
- D5/8
- E1/2
32Tile values in Scrabble.
In the game of Scrabble, there are 100 letters tiles with the distribution of point values given in Table. Let X be the point value of a random Scrabble tile. What is the mathematical expectation of X?
- A187
- B1,87
- C18,7
- D0,1817
- E19
33Tile values in Scrabble. In the game of Scrabble, there are 100 letters tiles with the distribution of point values given in Table. Let be the point value of a random Scrabble tile. What is the mathematical expectation of X^2?
- A1.87
- B4.71
- C3.26
- D5.2
- E9.1
34A fair six-sided die is tossed. You win $2 if the result is a «1», you win $1 if the result is a «6», but otherwise you lose $1. What is the dispersion of X?
- A1.74
- B1.47
- C-0.17
- D1.5
- E2.12
35A fair six-sided die is tossed. You win $2 if the result is a «1», you win $1 if the result is a «6» or «3», but otherwise you lose $1. What is the dispersion of ?
- A1.74
- B1.47
- C-0.17
- D1.5
- E2.12
36Which of the following is a discrete random variable?
- AThe time of waiting a train.
- BThe number of boys in family having 4 children.
- CA time of repair of TVs.
- DThe velocity in any direction of a molecule in gas.
- EThe height of a man.
37Which of the following is a discrete random variable?
- AThe time of waiting a train.
- BThe number of people in a community living to 100 years of age.
- CThe mistake of a rounding off of a number up to the whole number.
- DThe velocity in any direction of a molecule in gas.
- EThe amount of time (starting from now) until an earthquake occurs
38Two independent random variables X and Y are given by the following tables of distribution: Find the mathematical expectation of X+Y?
- A2.3
- B3.8
- C1
- D5.2
- E2.4
39Two independent random variables X and Y are given by the following tables of distribution: Find the mean square deviation of X+Y?
- A2.13
- B1.296
- C1.457
- D1.795
- E2.4
40Two independent random variables X and Y are given by the following tables of distribution: Find the mathematical expectation of XY?
- A-3.8
- B-3.36
- C-1.4
- D4.26
- E2.44
41A set of families has the following distribution on number of children: Determine x1, x2, if it is known that M(X) = 2, D(X) = 1.2?
- Ax1 = 1/3, x2 = 4/3
- Bx1 = 0, x2 = 1
- Cx1 = 0, x2 = 4/3
- Dx1 = 0, x2 = 10
- Ex1 = 1/3, x2 = -1
42The lifetime of a machine part has a continuous distribution on the interval (0, 30) with probability density function f(x) = c(10 + x)^(-2) . Calculate the probability that the lifetime of the machine part is less than 6.
- A30/53
- B1/2
- C31/35
- D13/28
- E1/17
43The lifetime of a machine part has a continuous distribution on the interval (0, 30) with probability density function f(x) = c(10 + x)^(-2) . Calculate the probability that the lifetime of the machine part is less than 5.
- A1/17
- B7/20
- C10/11
- D19/35
- E7/11
44A random variable X is given by the density function of distribution: Find the integral function of distribution of the random variable X?
- A
- B
- C
- D
- E
- A
45A random variable X is given by the density function of distribution: Find the integral function of distribution of the random variable X?
- A
- B
- C
- D
- E
- A
46вопрос уже был, тыкни на смайлик
- A:)
- B1
- C2
- D3
- E4
47A random variable X is given by the integral function of distribution: Find the mathematical expectation of the random variable X?
- A15/4
- B5
- C5/2
- D3/4
- E1
48вопрос уже был, нажми на смайлик ещё раз
- A:))
- B1
- C2
- D3
- E4
49A random variable X is given by the integral function of distribution: If , then find the dispersion of the random variable X?
- A1/3
- B1
- C0
- D3/4
- E-2/3
50Этот вопрос тоже уже был, улыбнись :)
- A:)))
- B1
- C2
- D3
- E4
51The lifetime in hours of a certain kind of radio tube is a random variable having a probability density function given by: What is the probability that exactly 1 of 5 such tubes in a radio set will have to be replaced within the first 150 hours of operation?
- A80/243
- B40/243
- C0
- D160/243
- E1/3
52The lifetime in hours of a certain kind of radio tube is a random variable having a probability density function given by: What is the probability that exactly 3 of 5 such tubes in a radio set will have to be replaced within the first 150 hours of operation?
- A80/243
- B40/243
- C0
- D160/243
- E1/3
53A random variable X is given by the integral function of distribution: Find the probability that random variable takes the values on (2, 6).
- A117/125
- B208/125
- C63/125
- D113/125
- E1/5
54A random variable X is given by the density function of distribution: Find the value of C?
- A2
- B-1
- C1
- D3
- E-3
55Ещё один вопрос повторился, найди смайлик :))))
- A:)
- B1
- C2
- D3
- E4
56A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| > 3.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
57Снова найди смайлик :")
- A:")
- B1
- C2
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58A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| > 3.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
59A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| <1.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
60A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| > 1.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
61A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| > 2.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
62A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| > 3.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
63A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| > 5.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
64A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| > 5.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
65A discrete random variable X is given by the following law of distribution: By using the Chebyshev inequality estimate the probability that |X – M(X)| <4.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
66The probability that a shooter will beat out 10 aces at one shot is equal to 0.1 and the probability to beat out 9 aces is equal to 0.3. Choose the correctly calculated probabilities of the events.
- AP(beat out more than 8 aces) = 0.5
- BP(beat out more than 10 aces) = 0.2
- CP(beat out 9 or less aces) = 0.9
- DP(beat out more than 9 aces) = 0.3
- EP(beat out 9 or more aces) = 0.3
67повтор
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- Bповтор-
- Cповтор--
- Dповтор---
- Eповтор----
68повтор
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- Bповтор-
- Cповтор--
- Dповтор---
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69Three students pass an exam. Let be the event «the exam will be passed on “excellent” by the i-th student» (i = 1, 2, 3). Which of the following events correctly expressed by and their negations?
- AA={exam will not be passed on "excellent" by only one student}
- BB={exam will not be passed on "excellent" by only two students}
- CC={exam will not be passed on "excellent" by at least two students}
- DD={exam will not be passed on "excellent" by three students}
- EE={exam will not be passed on "excellent" by three students}
70Three students pass an exam. Let be the event «the exam will be passed on “excellent” by the i-th student» (i = 1, 2, 3). Which of the following events correctly expressed by and their negations?
- AA={exam will not be passed on "excellent" by only one student}
- BB={exam will not be passed on "excellent" by only two students
- CC={exam will not be passed on "excellent" by at least two students}
- DD={exam will not be passed on "excellent" by three students
- EE={exam will not be passed on "excellent" by three students} (Все А под чертой)
71A random variable X is given by the integral function of distribution:
- AM(X) = 10
- BD(X) = 1/2
- CP(10 < X < 15) = 1/2
- DP(X < 0)
- EM(X) = 3/10
72повтор
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- B1
- C2
- D3
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73повтор
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- B1
- C2
- D3
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74The probability that a shooter hit in a target at one shot is equal to 0.8. The shooter has made 3 shots. Choose the correctly calculated probabilities of the events.
- AP(at least 1 of 3 shots will strike the target)=0.384
- BP(at least 1 of 3 shots will strike the target)=0.992
- CP(at least 2 of 3 shots will not strike the target)=0.189
- DP(at least 2 of 3 shots will strike the target)=0.845
- EP(neither of 3 shots will strike the target)=0.8
75повтор
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- Bок
- Cок1
- Dок2
- Eок3
76повтор
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- B1
- C2
- D3
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77повтор
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- B1
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78The probability to receive high dividends under shares at the first enterprise – 0.2, on the second – 0.35, on the third – 0.15. Choose the correctly calculated probabilities that a shareholder having shares of all the enterprises will receive high dividends.
- AP(at least on two enterprises) = 0,1315
- BP(at least on two enterprises) = 0,4214
- CP(only at one enterprise) = 0,7
- DP(at least on one enterprise) = 0,4265
- EP(exactly on three enterprises) = 0,105
79The probability to receive high dividends under shares at the first enterprise – 0.2, on the second – 0.2, on the third – 0.3. Choose the correctly calculated probabilities that a shareholder having shares of all the enterprises will receive high dividends.
- AP(only at one enterprise) = 0,416
- BP(only at one enterprise) = 0,7
- CP(at least on one enterprise) = 0,426
- DP(at least on two enterprises) = 0,354
- EP(exactly on three enterprises) = 0,105
80The first brigade has 6 tractors, and the second – 9. One tractor demands repair in each brigade. A tractor is chosen at random from each brigade. Choose the correctly calculated probabilities of events.
- AP(both chosen tractors demands repair)=1/54
- BP(one of the chosen tractors demands repair)=0.5
- CP(both chosen tractors demands repair)=0
- DP(both chosen tractors demands repair)=1/27
- EP(both chosen tractors are serviceable)=13/15
81The first brigade has 5 tractors, and the second – 8. One tractor demands repair in each brigade. A tractor is chosen at random from each brigade. Choose the correctly calculated probabilities of events.
- AP(one of the chosen tractors demands repair)=11/40
- BP(one of the chosen tractors demands repair)=7/40
- CP(both chosen tractors demands repair)=1/20
- DP(both chosen tractors demands repair)=1/2
- EP(both chosen tractors are serviceable)=1/3
82All of the letters that spell STUDENT are put into a bag. Choose the correctly calculated probabilities of events.
- AP(drawing a S, and then drawing a T)=1/21
- BP(drawing a T, and then drawing a D)=1/42
- CP(selecting a vowel, and then drawing a U)=1/42
- DP(selecting a vowel, and then drawing a K)=1/42
- EP(selecting a vowel, and then drawing a T)=3/42
83All of the letters that spell MISSISSIPPI are put into a bag. Choose the correctly calculated probabilities of events.
- AP(of selecting a vowel, and then after returning the letter also drawing a M)=4/121
- BP(of drawing an I, and then after returning the letter also drawing a M)=3/121
- CP(of selecting a vowel, and then after returning the letter also drawing an O)=4/121
- DP(of selecting a vowel, and then after returning the letter also drawing a P)=6/121
- EP(of drawing a M, and then after returning the letter also drawing a S)=1/121
84The first brigade has n tractors, and the second – m. One tractor demands repair in each brigade. A tractor is chosen at random from each brigade. Choose the correctly calculated probabilities of events.
- An=3, m=5, P(both chosen tractors demands repair)=1/15
- Bn=3, m=6, P(one of the chosen tractors demands repair)=7/12
- Cn=2, m=5, P(both chosen tractors demands repair)=0.3
- Dn=2, m=3, P(both chosen tractors demands repair)=1/3
- En=5, m=2, P(both chosen tractors are serviceable)=0.2
85A jar of marbles contains 4 blue marbles, 5 red marbles, 1 green marble, and 2 black marbles. A marble is chosen at random from the jar. After returning it again, a second marble is chosen.
Choose the correctly calculated probabilities of events.
- AP(green, and then red)=5/144
- BP(black, and then black)=1/12
- CP(red, and then black)=7/72
- DP(green, and then blue)=1/72
- EP(blue, and then blue)=1/6
86If each of the regions in each spinner is the same size. Choose the correctly calculated probabilities of spinning each spinner.
- AP(getting a red sweater)=1/12
- BP(getting a white sweatshirt)=1/6
- CP(getting a white sweater)=5/12
- DP(getting a blue sweatshirt)=7/12
- EP(getting a blue t-shirt)=1/6
87повтор
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- B1
- C2
- D3
- E4
88Mary is playing a game in which she rolls one die and spins a spinner. Choose the correctly calculated probabilities of spinning each spinner.
- AP(get the 1 and green)=0
- BP(get the 7 and red)=1/18
- CP(get the 3 and green)=1/18
- DP(get the 2 and black)=1/4
- EP(get the 1 and white)=1
89повтор
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90Find the Bernoulli formula.
- A1)
- B2)
- C3)
- D4)
- E5)
91Find the Bernoulli formula.
- A1)
- B2)
- C3)
- D4)
- E5)
92A coming up a grain stored in a warehouse is equal to 50%. What is the probability that the number of came up grains among 100 ones will make from up to pieces (a grain – зерно)?
- A1)
- B2)
- C3)
- D4)
- E5)
93The probability of striking a target by a shooter at one shot is equal to . Find the probability P that at 100 shots the target will be struck no less than a and no more b times.
- A1)
- B2)
- C3)
- D4)
- E5)
94The probability of striking a target by a shooter at one shot is equal to 1/4. Find the probability P that at 100 shots the target will be struck no less than and no more times.
- A1)
- B2)
- C3)
- D4)
- E5)
95Find approximately the probability that an event will happen exactly from to times at 400 trials if in each trial the probability of its occurrence is equal to 0.2.
- A
- B
- C
- D
- E
- A
96Find approximately the probability that an event will happen exactly from to times at 484 trials if in each trial the probability of its occurrence is equal to 0.5.
- A1
- B2
- C3
- D4
- E5
97A factory has sent 2500 good-quality products. The probability that one product has been damaged at a transportation is . Find the probability P that at the transportation it will be damaged from a to b products.
- A
- B
- C
- D
- E
- A
98Find the right inequation.
- A
- B
- C
- D
- E
- A
99Let X~Binomial(n, p). Find the right inequation.
- A
- B
- C
- D
- E
- A
100From past experience a professor knows that the test score of a student taking her final examination is a random variable with mean 75. Suppose, in addition, the professor knows that a variance of a student’s test score is equal to 25. Find the right inequation.
- AP(|X - 75| < 30) > 1/36
- BP(65 <= X <= 85) > 3/4
- CP(60 <= X <= 90) >= 1/9
- DP(X > 80) > 75/80
- EP(|X - 75| <= 45) < 80/81
101Find the right statements
- A
- B
- C
- D
- E
- A
102Find the false statements.
- A0 <= F(x) <= 1
- B
- C
- D
- E
103Find the false statements.
- A
- B
- C
- D
- E
- A
104Find the false inequations.
- A
- B
- C
- D
- E
- A
105Find the right property of distribution function.
- A
- B
- C
- D
- E
- A
106Find the right property of probability density.
- A
- B
- C
- D
- E
- A
107Let a series of distribution of a random variable be given: . What does this tell us about the random variable X?
- A
- B
- CM(X) = 1
- D
- ED(X) = 10
- A
108Let a series of distribution of a random variable be given: . What does this tell us about the random variable X?
- A
- B
- CM(X) = 4
- DD(X) = 22.2
- EM(X) = 9
- A
109Let a series of distribution of a random variable be given: . What does this tell us about the random variable X?
- A
- BD(X) = 1.09
- CD(X) = 1
- DM(X) = 2
- A
110Let a series of distribution of a random variable be given: . What does this tell us about the random variable X?
- A
- B
- C
- DD(X) = 1
- EM(X) = 0.1
- A
111Let a series of distribution of a random variable be given: . What does this tell us about the random variable X?
- A
- B
- CM(X^2) = 4
- DD(X) = 8
- ED(X) = 55
- A
112The probability of working each of four combines without breakages during a certain time is equal to 0,9. The random variable X – the number of combines working trouble-free. What does this tell us about the random variable X?
- AP(X = 0) = 0.1*
- BP(X = 3) = 0.0009
- CP(X = 1) = 0.0729
- DP(X = 2) = 0.0081
- EP(X = 0) = 0.001
113A die is tossed before the first landing “six” aces. Find the probability that the first appearance of “six” will take place at the n-th tossing the die?
- AP(n = 2) = 5/36
- B
- C
- D
- E
114A random variable X is distributed under an exponential law with parameter *lambda*. Find the probability of hit of the random variable X into the interval (a; b).
- A
- B
- C
- D
- E
- A
115The time (in hours) required to repair a machine is an exponentially distributed random variable with parameter *lambda* . Find the correctly calculated probabilities of the events.
- A
- B
- C
- D
- E
- A
116A random variable X is distributed under a normal law with mathematical expectation a = 20. The probability of hit of the random variable X into the interval (10, 30) is 0.6826. Find the correctly calculated probabilities of the events.
- A
- BD(X) = 100
- C
- D
- E
- A
117A normally distributed random variable X is given by the differential function: . Find the probability of hit of the random variable X into the interval (a; b).
- Aa = 2
- B
- CD(X) = 2
- D
- E
118Suppose that X is a normal law with mathematical expectation a = 5. The probability of hit of the random variable X into the interval (...) is 0.1587. Find the correctly calculated probabilities of the events.
- A
- BD(X) = 16
- C
- D
- E
- A
119Assuming that the height of men of a certain age group is a normally distributed random variable X with the parameters *........*. Find the correctly calculated probabilities of the events.
- AP(176; 182) = 0.1348
- B
- C
- D
- E
120Assuming that the height of men of a certain age group is a normally distributed random variable X with the parameters . Find the correctly calculated probabilities of the events.
- AP(176; 182) = 0.1348
- BP(20; 30) = 10/30
- C
- D
- EP(10; 50) = 0.2417
Informações
- Descrição
- Quiz sobre TBMS, criado por Mark Kim em 20-12-2019.
- Autor
- Mark Kim
- Idioma
- English
- Visualizações
- 36
- Avaliação
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