Reshebnik Ryabushko. Solved IDZ 18.2, Option 15
Replenishment date: 07.11.2018
Content: 15v-IDZ18.2.rar (78.91 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)
1.15. Two workers producing the same type of product allow the production of second-grade products with probabilities equal to 0,4 and 0,3, respectively. Each worker has 2 items taken; CB X - the number of products of the second grade among them.
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.
3.15. From point C, a gun is being fired along a straight line SK. It is assumed that the flight range is normally distributed with a mathematical expectation of 1000 m and a standard deviation of 5 m.Determine (in percent) how many projectiles will fall with a flight from 5 to 70 m. (The calculated answer is 15,9% or if you round up 16%)
4. Solve the following tasks.
4.15. The probability of an event occurring in a single trial is 0,6. Using Bernoulli's theorem, determine the number of independent trials, starting from which the probability of deviation of the event frequency from its probability in absolute value less than 0,1 is greater than 0,97. (Answer: 800)
1.15. Two workers producing the same type of product allow the production of second-grade products with probabilities equal to 0,4 and 0,3, respectively. Each worker has 2 items taken; CB X - the number of products of the second grade among them.
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.
3.15. From point C, a gun is being fired along a straight line SK. It is assumed that the flight range is normally distributed with a mathematical expectation of 1000 m and a standard deviation of 5 m.Determine (in percent) how many projectiles will fall with a flight from 5 to 70 m. (The calculated answer is 15,9% or if you round up 16%)
4. Solve the following tasks.
4.15. The probability of an event occurring in a single trial is 0,6. Using Bernoulli's theorem, determine the number of independent trials, starting from which the probability of deviation of the event frequency from its probability in absolute value less than 0,1 is greater than 0,97. (Answer: 800)
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.