3 Semester Test: Probability theory and mathematical h

3 Semester Test: Probability theory and mathematical statistics


Exercise 1
Question 1. What event in the terminology of the theory of probability is to hit the target when firing at a shooting range?
Question 2. Suppose that event A k during the tests took place s times. What is the absolute frequency of the event A?
Question 3. In six throws of the dice (cube with numbers from 1 to 6 at the edges), the figure has fallen 2 times 5, the figure fell 4 2 times, and the numbers 3 and 2 fell 1 time each. What the results of this observation relative frequency (relative frequency) events consisting of dropping numbers 3 or 4 digits?
Question 4. What is the statistical definition of probability?
Question 5. What event is authentic?

Task 2
Question 1. In which case the system is called a complete event?

Question 2. Assume that some tests may be events A and B, the probability of an event A, the probability of the event A is incompatible with B. Which of the following statements is not always true?
Question 3. What is the probability that the three throws of the dice falls three times the number 3?
Question 4. From an urn in which four white balls and 3 black randomly extract two balls. (After removing the ball is not returned in the box). The balls in the urn differ only in color. What is the probability that the first black ball will be ejected, and the second - white?
Question 5. If you get a bullet in the target, it topples. For example, 35.
1. 43.
Question 4. Which of the following statements is true in the absence of the effect of repeated treatments for paired observations of random variables X and Y, regardless of their distribution?
1. for all.
2. for all.
3. for all.
4. for all.
5. .
Question 5. What is the condition necessary for the application of the criterion of sign Wilcoxon rank sum?
1. for all.
2. Random variables, which are continuous and equally distributed.
3. Random variables where discrete.
4. Random variables, which have a different distribution.
5. Implementation of the hypothesis of no effect of treatment.
ETC
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