Mat II

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Question 1 of 42

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 ?

Select one of the following:

Explanation

Question 2 of 42

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.

Select one of the following:

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

Explanation

Question 3 of 42

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.

Select one of the following:

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

Explanation

Question 4 of 42

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?

Select one of the following:

Explanation

Question 5 of 42

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

Select one of the following:

Explanation

Question 6 of 42

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

Select one of the following:

15/4
5
5/2
3/4
1

Explanation

Question 7 of 42

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

Select one of the following:

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

Explanation

Question 8 of 42

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?

Select one of the following:

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

Explanation

Question 9 of 42

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?

Select one of the following:

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

Explanation

Question 10 of 42

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

Select one of the following:

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

Explanation

Question 11 of 42

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

Select one of the following:

2
-1
1
3
-3

Explanation

Question 12 of 42

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.

Select one of the following:

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

Explanation

Question 13 of 42

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.

Select one of the following:

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

Explanation

Question 14 of 42

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.

Select one of the following:

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

Explanation

Question 15 of 42

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.

Select one of the following:

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

Explanation

Question 16 of 42

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.

Select one of the following:

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

Explanation

Question 17 of 42

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.

Select one of the following:

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

Explanation

Question 18 of 42

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.

Select one of the following:

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

Explanation

Question 19 of 42

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.

Select one of the following:

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

Explanation

Question 20 of 42

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.

Select one of the following:

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

Explanation

Question 21 of 42

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.

Select one of the following:

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

Explanation

Question 22 of 42

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.

Select one of the following:

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

Explanation

Question 23 of 42

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?

Select one of the following:

Explanation

Question 24 of 42

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.

Select one of the following:

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

Explanation

Question 25 of 42

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.

Select one of the following:

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

Explanation

Question 26 of 42

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.

Select one of the following:

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

Explanation

Question 27 of 42

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.

Select one of the following:

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

Explanation

Question 28 of 42

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.

Select one of the following:

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

Explanation

Question 29 of 42

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.

Select one of the following:

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

Explanation

Question 30 of 42

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

Select one of the following:

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

Explanation

Question 31 of 42

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

Select one of the following:

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

Explanation

Question 32 of 42

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.

Select one of the following:

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

Explanation

Question 33 of 42

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.

Select one of the following:

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

Explanation

Question 34 of 42

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

Select one of the following:

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

Explanation

Question 35 of 42

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.

Select one of the following:

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

Explanation

Question 36 of 42

90. Find the Bernoulli formula.

Select one of the following:

Explanation

Question 37 of 42

92. A 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)?

Select one of the following:

Explanation

Question 38 of 42

93. The probability of striking a target by a shooter at one shot is equal to 3/4 . Find the probability P
that at 100 shots the target will be struck no less than a and no more b times.

Select one of the following:

Explanation

Question 39 of 42

94. The 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 a and no more b times.

Select one of the following:

Explanation

Question 40 of 42

95. Find approximately the probability that an event will happen exactly from a to b times at 400
trials if in each trial the probability of its occurrence is equal to 0.2.

Select one of the following:

Explanation

Question 41 of 42

96. Find approximately the probability that an event will happen exactly from a to b times at 484
trials if in each trial the probability of its occurrence is equal to 0.5.

Select one of the following:

Explanation

Question 42 of 42

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.

Select one of the following:

Explanation

Check answer

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	Created by hoffa HOFFMAN almost 5 years ago

Quiz on Mat II, created by hoffa HOFFMAN on 27/12/2019.

Mat II

Question 1 of 42

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 ?

Select one of the following:

Explanation

Question 2 of 42

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.

Select one of the following:

Explanation

Question 3 of 42

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.

Select one of the following:

Explanation

Question 4 of 42

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?

Select one of the following:

Explanation

Question 5 of 42

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

Select one of the following:

Explanation

Question 6 of 42

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

Select one of the following:

Explanation

Question 7 of 42

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

Select one of the following:

Explanation

Question 8 of 42

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?

Select one of the following:

Explanation

Question 9 of 42

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?

Select one of the following:

Explanation

Question 10 of 42

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

Select one of the following:

Explanation

Question 11 of 42

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

Select one of the following:

Explanation

Question 12 of 42

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.

Select one of the following:

Explanation

Question 13 of 42

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.

Select one of the following:

Explanation

Question 14 of 42

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.

Select one of the following:

Explanation

Question 15 of 42

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.

Select one of the following:

Explanation

Question 16 of 42

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.

Select one of the following:

Explanation

Question 17 of 42

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.

Select one of the following:

Explanation

Question 18 of 42

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.

Select one of the following:

Explanation

Question 19 of 42

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.

Select one of the following:

Explanation

Question 20 of 42

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.

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 ?

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.

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.

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

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

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?

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?

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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?

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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

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.

92. A 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)?