Reshebnik Ryabushko. Solved IDZ 18.2, Option 17

1. Find the distribution law of the indicated discrete CB X and its distribution function F (x). Calculate the mathematical expectation M (X), variance D (X) and standard deviation σ (X). Plot the distribution function F (x)

1.17. The probability of device failure during the reliability test is 0,2; SV X - the number of devices that failed in operation, among the five tested.

2. Given the distribution function F (x) RV X. Find the probability density f (x), mathematical expectation M (X), variance D (X) and the probability of falling RV X on the segment [a; b]. Build graphs of functions F (x) and f (x).

3. Solve the following tasks.
3.17. Trams on this route run every 5 minutes. A passenger arrives at a tram stop at some point in time. What is the probability of a passenger appearing not earlier than 1 minute after the departure of the previous tram, but not later than 2 minutes before the departure of the next tram?

4. Solve the following tasks.
4.17. The mathematical expectation of the amount of precipitation falling during the year in a given area is 60 cm. Determine the probability that at least 180 cm of precipitation will fall in this area.