DHS 18.2 - Option 8. Decisions Ryabushko AP

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)

1.8. The probability of a call is received on the ATS for 1 minute is equal to 0.4; NE X- number of calls received by the PBX for 4 minutes.

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.
3.8. It is believed that the product - high quality, if the deviation from its nominal size is not greater than the absolute value of 3.6 mm. Random deviations from the nominal size of the product are subject to a normal distribution with standard deviation equal to 3 mm. Systematic deviations are not available. Determine the average of the highest quality products to the 100 made.

4. Solve the following problems.
4.8. The probability that a randomly selected part will be defective, in each test is the same and equal to 0.1. Part of products is not taken upon detection of at least 10 defective items. What is necessary to check the details in order to with probability 0.6 it could be argued that the party, which has 10% of marriage will not be accepted?