DHS 18.2 - Option 18. 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)

1.18. In the first box 10 seals, 2 of them are defective, the second - 16, 4 of them are defective, in the third - 12 seals, including 3 defective; SW X - number of defective seals on the condition that each of the boxes taken randomly in one gland.

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.
3.18. The minute hand of the clock moves abruptly at the end of each minute. Find the probability that a given instant the clock shows a time which differs from the true by no more than 20 seconds.

4. Solve the following problems.
4.18. As a result, 200 independent experiments found values SW X1, X2, ..., X200 and M (X) = D (X) = 2. Rate on top of the probability that the absolute value of the difference between the arithmetic mean value of a random variable; and the expectation is less than 0.2.