DHS 18.2 - Option 28. 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)

1.28. The failure of the gearbox takes place for three main reasons: failure of gear teeth, the unacceptably high contact stresses and excessive rigidity. Each of the causes leading to breakage of the gearbox with the same probability of 0.1; SW X - number of reasons that led to the failure in one trial.

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.
3.28. The growth of males is a random variable distributed according to a normal distribution with mean equal to 170 cm, and a variance equal to 49 cm2. Find the probability that the three randomly selected men will have a height of 170 to 175 cm.

4. Solve the following problems.
4.28. The expectation of deviation from the center of the target when firing on it is 6 cm. To assess the probability that the target shooting in a circular radius of 15 cm will hit the target.