# DHS 18.2 - Option 10. 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)

1.10. The probability of successful completion of the first examination for the students is 0.9, the second exam - 0.8, the third - 0.7; SW X - the number of exam passes.

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.
3.10. SW X obeys a normal law with expectation of 0. The probability of hitting this NE in the interval (-1, 1) is equal to 0.5. Find the standard deviation and record the normal law.

4. Solve the following problems.
4.10. The probability of occurrence of an event in one experiment is 0.6. What is the probability that this event will be in the majority of the 60 trials?