Reshebnik Ryabushko. Solved IDZ 18.2, Option 21
Replenishment date: 07.11.2018
Content: 21v-IDZ18.2.rar (83.17 KB)
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Description
1. Find the distribution law of the indicated discrete CB X and its distribution function F (x). Calculate the mathematical expectation M (X), variance D (X) and standard deviation σ (X). Plot the distribution function F (x)
1.21. In the first student group of 24 people there are 4 excellent students, in the second of 22 - 3 excellent students, in the third of 24 - 6 excellent students and in the fourth of 20 - 2 excellent students; SV X is the number of honors invited to the conference, provided that one person was selected at random from each group.
2. Given the distribution function F (x) RV X. Find the probability density f (x), mathematical expectation M (X), variance D (X) and the probability of falling RV X on the segment [a; b]. Build graphs of functions F (x) and f (x).
3. Solve the following tasks.
3.21. The substance is weighed without systematic errors. The random weighing error is normally distributed with a mathematical expectation of 20 kg and a standard deviation of 2 kg. Find the probability that the next weighing differs from the mathematical expectation by no more than 100 g.
4. Solve the following tasks.
4.21. The number of flat screen TVs averages 40% of their total production. Using Chebyshev's inequality, estimate the probability that, in a batch of 500 TVs, the share of flat-screen TVs deviates from the average by no more than 0,06.
1.21. In the first student group of 24 people there are 4 excellent students, in the second of 22 - 3 excellent students, in the third of 24 - 6 excellent students and in the fourth of 20 - 2 excellent students; SV X is the number of honors invited to the conference, provided that one person was selected at random from each group.
2. Given the distribution function F (x) RV X. Find the probability density f (x), mathematical expectation M (X), variance D (X) and the probability of falling RV X on the segment [a; b]. Build graphs of functions F (x) and f (x).
3. Solve the following tasks.
3.21. The substance is weighed without systematic errors. The random weighing error is normally distributed with a mathematical expectation of 20 kg and a standard deviation of 2 kg. Find the probability that the next weighing differs from the mathematical expectation by no more than 100 g.
4. Solve the following tasks.
4.21. The number of flat screen TVs averages 40% of their total production. Using Chebyshev's inequality, estimate the probability that, in a batch of 500 TVs, the share of flat-screen TVs deviates from the average by no more than 0,06.
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.