Mat II

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 ?

• a

• b

• c

• d

• e

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.

• 30/53

• 1/2

• 31/35

• 13/28

• 1/17

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.

• 1/17

• 7/20

• 10/11

• 19/35

• 7/11

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?

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

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

• 15/4

• 5

• 5/2

• 3/4

• 1

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

• 1/3

• 1

• 0

• 3/4

• -2/3

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?

• 80/243

• 40/243

• 0

• 160/243

• 1/3

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

• 117/125

• 208/125

• 63/125

• 113/125

• 1/5

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

• 2

• -1

• 1

• 3

• -3

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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.

• 1

• 2/3

• 1/6

• 1/4

• -1/2

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?

• 1

• 2

• 3

• 4

• 5

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.

• M (X) = 10

• D(X) = 1/2

• P (10 < X < 15) = 1/2

• P (X < 0) = 0

• M (X) = 3/10

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.

• 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

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

• 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

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.

• 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

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)?

• 1

• 2

• 3

• 4

• 5

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.

• 1

• 2

• 3

• 4

• 5

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.

• 1

• 2

• 3

• 4

• 5

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.

• 1

• 2

• 3

• 4

• 5

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.

• 1

• 2

• 3

• 4

• 5

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.

• 1

• 2

• 3

• 4

• 5