Reshebnik Ryabushko. Solved IDZ 18.2, Option 18
Replenishment date: 07.11.2018
Content: 18v-IDZ18.2.rar (75.61 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)
1.18. In the first box there are 10 oil seals, of which 2 are defective, in the second - 16, of which 4 are defective, in the third - 12 oil seals, of which 3 are defective; CB X - the number of defective oil seals, provided that one oil seal is taken at random from each box.
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.
3.18. The minute hand of the watch jumps at the end of each minute. Find the probability that at a given moment the clock will show a time that differs from the true one by no more than 20 s.
4. Solve the following tasks.
4.18. As a result of 200 independent experiments, the values of SV X1, X2, ..., X200 were found, with M (X) = D (X) = 2. Estimate from above the probability that the absolute value of the difference between the arithmetic mean of the values of the random variable; and the mathematical expectation is less than 0,2.
1.18. In the first box there are 10 oil seals, of which 2 are defective, in the second - 16, of which 4 are defective, in the third - 12 oil seals, of which 3 are defective; CB X - the number of defective oil seals, provided that one oil seal is taken at random from each box.
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.
3.18. The minute hand of the watch jumps at the end of each minute. Find the probability that at a given moment the clock will show a time that differs from the true one by no more than 20 s.
4. Solve the following tasks.
4.18. As a result of 200 independent experiments, the values of SV X1, X2, ..., X200 were found, with M (X) = D (X) = 2. Estimate from above the probability that the absolute value of the difference between the arithmetic mean of the values of the random variable; and the mathematical expectation is less than 0,2.
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.