# DHS 18.2 - Option 2. Decisions Ryabushko AP

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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)

1.2. Produce three shots on target. Probability of hitting the target with the first shot is 0.4 second - 0.5, the third - 0.6; SW X - number of target lesions.

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.
3.2. In determining the distance by radar random errors are distributed by the normal law. What is the probability that the error in determining the distance exceeds 20 m, it is known that systematic errors do not allow the radar, and the error variance is 1370 m2?

4. Solve the following problems.
4.2. The variance of each of the 4,500 independent and identically distributed random variables is equal to 5. Find the probability that the arithmetic mean of these random variables will deviate from its mathematical expectation of no more than 0.04.