DHS 18.2 - Option 21. 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)

1.21. In the first group of students from 24 people 4 honors, the second from 22 - 3 honors, the third of 24 - 6 honors and fourth out of 20 - 2 honors; SW X - number of standouts invited to the conference, with the proviso that each group allocated randomly by one person.

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.
3.21. Produce weighting agent without systematic errors. Random weighing error is normally distributed with a mean of 20 kg and a standard deviation of 2 kg. Find the probability that the next weighting differs from the expectation of not more than 100 g

4. Solve the following problems.
4.21. The number of flat-screen TVs on average 40% of their total output. Using Chebyshev inequality, estimate the probability that the batch of 500 televisions share with flat-screen TVs deviates from the average by no more than 0.06.