Reshebnik Ryabushko. Solved IDZ 18.2, Option 1
Replenishment date: 07.11.2018
Content: 1v-IDZ18.2.rar (77.75 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)
1.1. The car must drive along a street with four independently operating traffic lights. Each traffic light gives red and green signals with an interval of 2 minutes; CB X is the number of car stops on this street.
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.
3.1. A roller made by an automatic machine is considered standard if the deviation of its diameter from the design size does not exceed 2 mm. Random deviations of the roll diameters obey the normal law with a standard deviation of 1,6 mm and a mathematical expectation of 0. How many standard rolls (in percent) does the machine make?
4. Solve the following tasks.
4.1. To determine the quality of the products manufactured by the plant, 2500 items were selected at random. Among them, there were 50 with defects. The frequency of manufacturing defective products is taken as an approximate value of the probability of manufacturing defective products. Determine the probability with which it can be guaranteed that the absolute error allowed in this case will not exceed 0,02.
1.1. The car must drive along a street with four independently operating traffic lights. Each traffic light gives red and green signals with an interval of 2 minutes; CB X is the number of car stops on this street.
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.
3.1. A roller made by an automatic machine is considered standard if the deviation of its diameter from the design size does not exceed 2 mm. Random deviations of the roll diameters obey the normal law with a standard deviation of 1,6 mm and a mathematical expectation of 0. How many standard rolls (in percent) does the machine make?
4. Solve the following tasks.
4.1. To determine the quality of the products manufactured by the plant, 2500 items were selected at random. Among them, there were 50 with defects. The frequency of manufacturing defective products is taken as an approximate value of the probability of manufacturing defective products. Determine the probability with which it can be guaranteed that the absolute error allowed in this case will not exceed 0,02.
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.