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Mat II
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Questions in this quiz (42)
141. 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 ?
- Aa
- Bb
- Cc
- Dd
- Ee
242. 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.
- A30/53
- B1/2
- C31/35
- D13/28
- E1/17
343. 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.- A1/17
- B7/20
- C10/11
- D19/35
- E7/11
444. A random variable X is given by the density function of distribution:n Find the integral function of distribution of the random variable X?
- A
- B
- C
- D
- E
- A
545. A 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
647. A 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
749. A 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
851. 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?
- A80/243
- B40/243
- C0
- D160/243
- E1/3
952. 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?- A80/243
- B40/243
- C0
- D160/243
- E1/3
1053. A random variable X is given by the integral function of distribution:
Find the probability that random variable takes the values on .
- A117/125
- B208/125
- C63/125
- D113/125
- E1/5
1154. A random variable X is given by the density function of distribution:
Find the value of C?
- A2
- B-1
- C1
- D3
- E-3
1256. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
1357. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
1458. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
1559. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
1660. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
1761. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
1862. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
1963. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
2064. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
2165. 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.
- A1
- B2/3
- C1/6
- D1/4
- E-1/2
2266. 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.- 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 9 or less aces) = 0.3
- EP(beat out 9 or more aces) = 0.3
2369. 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?
- A1
- B2
- C3
- D4
- E5
2471. 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.
- AM (X) = 10
- BD(X) = 1/2
- CP (10 < X < 15) = 1/2
- DP (X < 0) = 0
- EM (X) = 3/10
2574. 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.- 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
2678. 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.- AP(at least on two enterprises) = 0.1315
- BP(exactly 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
2779. 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.- 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
2880. 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.- 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
2981. 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.- 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
3082. All 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
3183. All 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
3284. 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.- 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
3385. 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.
- 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
3486. If 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
3588. Mary 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
3690. Find the Bernoulli formula.
- A
- B
- C
- D
- E
- A
3792. 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)?
- A1
- B2
- C3
- D4
- E5
3893. 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.
- A1
- B2
- C3
- D4
- E5
3994. 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.
- A1
- B2
- C3
- D4
- E5
4095. 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.
- A1
- B2
- C3
- D4
- E5
4196. 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.
- A1
- B2
- C3
- D4
- E5
4297. 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.
- A1
- B2
- C3
- D4
- E5
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- Quiz on Mat II, created by hoffa HOFFMAN on 27/12/2019.
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- hoffa HOFFMAN
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