DHS 18.2 - Option 27. 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)

1.27. The party of 25 products 6 defective. To control the quality of their randomly selected four products; SW X - the number of defective items among the selected.

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.
3.27. It is believed that the length of the deviation from the standard of manufactured parts is a random variable distributed according to the normal law. Knowing that the sub-length of 40 cm, a standard deviation of 0.4 cm, to determine what length of the article accuracy can be ensured with a probability of 0.8.

4. Solve the following problems.
4.27. The number of sunny days in a year for a given area is a random variable whose expectation is equal to 75 days. Rate the likelihood that in the course of the year in this area will be more than 200 days of sunshine.