ИДЗ 18.2 – Вариант 6. Решения Рябушко А.П.

1. Find the distribution of the said discrete CB X and its distribution function F (x). Calculate the expectation M (X), the variance of D (X) and standard deviation σ (X). Draw the graph of the distribution function F (x)

1.6. The probability of fulfillment of the plan for the SU-1 is equal to 0.9, for the SU-2 - 0.8, for SU-3 - 0.7; SW X - the number of SU, exceeded the plan.

2. Dana distribution function F (x) DM X. Find the probability density function f (x), the expectation M (X), the variance of D (X), and the probability of hitting NE X on the interval [a; b]. Construct the graphs of the functions F (x) and f (x).

3. Solve the following problems.
3.6. The flow of applications received by the telephone exchange, is the simplest Poisson flow. The expected number of calls is equal to 1 h 30. Find the probability that arrive for 1 min at least two calls.

4. Solve the following problems.
4.6. DM X is the average of 10,000 independent identically distributed random variables, the standard deviation of each of which is equal to 2. What is the maximum deviation of CB X from its mathematical expectation can be expected with a probability of not less than 0.9544?

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