DHS 18.2 - Option 15. 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)

1.15. Two workers producing the same type of products, allow the production of second-class products with probabilities equal to 0.4 and 0.3 respectively. Each worker is taken on 2 products; SW X - the number of second-class products among them.

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.
3.15. From point C being the firing of the guns along the line SC. It is assumed that the range is normally distributed with a mean of 1000 m and a standard deviation of 5 m. Determine the (percentage) as shells fall with flight from 5 to 70 m.

4. Solve the following problems.
4.15. The probability of occurrence of an event in a separate trial is 0.6. Applying Bernoulli´s theorem to determine the number of independent trials, at which the probability of the event frequency deviation from its probability in absolute value is less than 0.1, more than 0.97.