Mat II

Question 1

Question

41. A set of families has the following distribution on number of children: x1, x2 Determine , if it is known that M(x) = 2 D(x) =1.2 ?

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14 (binary/octet-stream)

Answer

Question 2

Question

42. The lifetime of a machine part has a continuous distribution on the interval (0, 30) with probability density function Calculate the probability that the lifetime of the machine part is less than 6.

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15 (binary/octet-stream)

Answer

30/53
1/2
31/35
13/28
1/17

Question 3

Question

43. The lifetime of a machine part has a continuous distribution on the interval (0, 11) with probability density function Calculate the probability that the lifteime of the machine part is less than 5.

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15 (binary/octet-stream)

Answer

1/17
7/20
10/11
19/35
7/11

Question 4

Question

44. A random variable X is given by the density function of distribution:n Find the integral function of distribution of the random variable X?

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16 (binary/octet-stream)

Answer

Question 5

Question

45. A random variable X is given by the density function of distribution: Find the integral function of distribution of the random variable X?

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Answer

Question 6

Question

47. A random variable X is given by the integral function of distribution: Find the mathematical expectation of the random variable X?

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30 (binary/octet-stream)

Answer

15/4
5
5/2
3/4
1

Question 7

Question

49. A random variable X is given by the integral function of distribution: If , then find the dispersion of the random variable X?

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31 (binary/octet-stream)

Answer

1/3
1
0
3/4
-2/3

Question 8

Question

51. The 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?

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32 (binary/octet-stream)

Answer

80/243
40/243
0
160/243
1/3

Question 9

Question

52. The 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?

Answer

80/243
40/243
0
160/243
1/3

Question 10

Question

53. A random variable X is given by the integral function of distribution: Find the probability that random variable takes the values on .

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33 (binary/octet-stream)

Answer

117/125
208/125
63/125
113/125
1/5

Question 11

Question

54. A random variable X is given by the density function of distribution: Find the value of C?

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34 (binary/octet-stream)

Answer

2
-1
1
3
-3

Question 12

Question

56. A 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.

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34 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 13

Question

57. A 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.

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1 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 14

Question

58. A 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.

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1 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 15

Question

59. A 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.

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2 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 16

Question

60. A 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.

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3 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 17

Question

61. A 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.

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4 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 18

Question

62. A 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.

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5 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 19

Question

63. A 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.

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6 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 20

Question

64. A 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.

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7 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 21

Question

65. A 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.

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8 (binary/octet-stream)

Answer

1
2/3
1/6
1/4
-1/2

Question 22

Question

66. The 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.

Answer

P(beat out more than 8 aces) = 0.5
P(beat out more than 10 aces) = 0.2
P(beat out 9 or less aces) = 0.9
P(beat out 9 or less aces) = 0.3
P(beat out 9 or more aces) = 0.3

Question 23

Question

69. Three 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?

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Answer

Question 24

Question

71. A random variable X is given by the integral function of distribution: What does this tell us about the random variable X? More than one option may be correct.

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10 (binary/octet-stream)

Answer

M (X) = 10
D(X) = 1/2
P (10 < X < 15) = 1/2
P (X < 0) = 0
M (X) = 3/10

Question 25

Question

74. The 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.

Answer

P(at least 1 of 3 shots will strike the target)=0.384
P(at least 1 of 3 shots will strike the target)=0.992
P(at least 2 of 3 shots will not strike the target)=0.189
P(at least 2 of 3 shots will strike the target)=0.845
P(neither of 3 shots will strike the target)=0.8

Question 26

Question

78. The 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.

Answer

P(at least on two enterprises) = 0.1315
P(exactly on two enterprises) = 0.4214
P(only at one enterprise) = 0.7
P(at least on one enterprise) = 0.4265
P(exactly on three enterprises) = 0.105

Question 27

Question

79. The 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.

Answer

P(only at one enterprise)=0.416
P(only at one enterprise)=0.7
P(at least on one enterprise)=0.426
P(at least on two enterprises)=0.354
P(exactly on three enterprises)=0.105

Question 28

Question

80. The 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.

Answer

P(both chosen tractors demands repair)=1/54
P(one of the chosen tractors demands repair)=0.5
P(both chosen tractors demands repair)=0
P(both chosen tractors demands repair)=1/27
P(both chosen tractors are serviceable)=13/15

Question 29

Question

81. The 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.

Answer

P(one of the chosen tractors demands repair)=11/40
P(one of the chosen tractors demands repair)=7/40
P(both chosen tractors demands repair)=1/20
P(both chosen tractors demands repair)=1/2
P(both chosen tractors are serviceable)=1/3

Question 30

Question

82. All of the letters that spell STUDENT are put into a bag. Choose the correctly calculated probabilities of events.

Answer

P(drawing a S, and then drawing a T)=1/21
P(drawing a T, and then drawing a D)=1/42
P(selecting a vowel, and then drawing a U)=1/42
P(selecting a vowel, and then drawing a K)=1/42
P(selecting a vowel, and then drawing a T)=3/42

Question 31

Question

83. All of the letters that spell MISSISSIPPI are put into a bag. Choose the correctly calculated probabilities of events.

Answer

P(of selecting a vowel, and then after returning the letter also drawing a M)=4/121
P(of drawing an I, and then after returning the letter also drawing a M)=3/121
P(of selecting a vowel, and then after returning the letter also drawing an O)=4/121
P(of selecting a vowel, and then after returning the letter also drawing a P)=6/121
P(of drawing a M, and then after returning the letter also drawing a S)=1/121

Question 32

Question

84. The first brigade has tractors n , 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.

Answer

n=3, m=5, P(both chosen tractors demands repair)=1/15
n=3, m=6, P(one of the chosen tractors demands repair)=7/12
n=2, m=5, P(both chosen tractors demands repair)=0.3
n=2, m=3, P(both chosen tractors demands repair)=1/3
n=5, m=2, P(both chosen tractors are serviceable)=0.2

Question 33

Question

85. A 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.

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11 (binary/octet-stream)

Answer

P(green, and then red)=5/144
P(black, and then black)=1/12
P(red, and then black)=7/72
P(green, and then blue)=1/72
P(blue, and then blue)=1/6

Question 34

Question

86. If each of the regions in each spinner is the same size. Choose the correctly calculated probabilities of spinning each spinner.

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12 (binary/octet-stream)

Answer

P(getting a red sweater)=1/12
P(getting a white sweatshirt)=1/6
P(getting a white sweater)=5/12
P(getting a blue sweatshirt)=7/12
P(getting a blue t-shirt)=1/6

Question 35

Question

88. Mary is playing a game in which she rolls one die and spins a spinner. Choose the correctly calculated probabilities of spinning each spinner.

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13 (binary/octet-stream)

Answer

P(get the 1 and green)=0
P(get the 7 and red)=1/18
P(get the 3 and green)=1/18
P(get the 2 and black)=1/4
P(get the 1 and white)=1

97. A factory has sent 2500 good-quality products. The probability that one product has been damaged at a transportation is 1/5 . Find the probability P that at the transportation it will be damaged from to products.

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25 (binary/octet-stream)

Answer

	Created by hoffa HOFFMAN almost 5 years ago

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