Theory of Probability and Mathematical Statistics
Replenishment date: 15.07.2023
Content: Answers. Probability theory and mathematical statistics.pdf (501.22 KB)
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1. Based on 20 observations, it was found that the sample fraction of the variance of the random variable y, caused by the variation of x, will be 81%. What is the sample pair correlation coefficient:
2. The unbiased estimate of the residual variance in the two-dimensional regression model is calculated by the formula:
3. The null hypothesis is:
4. The null hypothesis is rejected if:
5. What determines the accuracy of estimating the general share or probability when constructing a confidence interval in the case of a large sample size?
6. What determines the accuracy of estimating the general mean when constructing a confidence interval in the case of a known general variance?
7. What determines the accuracy of estimating the general mean when constructing a confidence interval in the case of an unknown general variance?
8. What determines the number of degrees of freedom in Student's distribution?
9. An estimate of the regression coefficient at x of the two-dimensional linear regression equation Y for X is found by the formula:
10. The pairwise correlation coefficient between variables is -1.
11. The pair correlation coefficient between variables is 1. This means:
12. Throw a dice. Find the probability of getting a face with 1 or 3 points:
13. Throw a dice. Find the probability of getting a face with 6 points:
14. Throw a dice. Find the probability of getting a face with an odd number of points:
15. Throw a dice. Find the probability of getting a face with an even number of points:
16. In tasks for calculating the probability that in n independent trials event A will appear from a to b times, it is used with a large number of trials and probability p different from 0 and 1:
17. In problems for calculating the probability that in n independent trials the event A will appear exactly m times, it is used with a large number of trials and a small probability p:
18. In tasks for calculating the probability that in n independent trials event A will appear exactly m times, it is used with a large number of trials and probability p different from 0 and 1:
19. What are the limits of the probability of occurrence of a random event?
20. Within what limits does the multiple coefficient of determination change?
21. Within what limits does the multiple correlation coefficient change?
22. Within what limits does the pair correlation coefficient change?
23. Within what limits does the partial correlation coefficient change?
24. Which of these concepts of combinatorics includes all elements of the set under study?
25. In what criterion is the G-distribution used?
26. In what criterion is the normal distribution used?
27. What criterion uses the Pearson distribution?
28. What criterion uses Student's distribution?
29. What criterion uses the Fischer-Snedekor distribution?
30. There are 12 standard and 3 defective parts in a box. Take out 1 item. Find the probability that this part is standard.
31. There are 12 standard and 3 defective parts in a box. Take out 1 item. Find the probability that this part is defective.
32. There are 4 standard and 2 defective parts in a box. Two parts are taken out in a row, while not returning them back to the box. Find the probability that both parts taken out are defective.
33. There are 4 standard and 2 defective parts in a box. Two parts are taken out one by one, and each time they are returned back to the box. Find the probability that both parts taken out are defective.
34. In a bunch of 10 similar keys from safes. Determine the probability with which the first randomly selected keys can open a safe with two sequentially opening locks.
35. In the theory of statistical evaluation, estimates are:
36. There are 2 white and 3 black balls in an urn. Take out the ball. Find the probability that this ball is white
37. There are 2 white and 3 black balls in an urn. Two balls are drawn in a row, and each time the balls are returned back to the basket. Find the probability that both balls drawn are white.
38. There are 2 white and 3 black balls in an urn. Two balls are taken out in a row, while the balls are not returned back to the basket. Find the probability of
2. The unbiased estimate of the residual variance in the two-dimensional regression model is calculated by the formula:
3. The null hypothesis is:
4. The null hypothesis is rejected if:
5. What determines the accuracy of estimating the general share or probability when constructing a confidence interval in the case of a large sample size?
6. What determines the accuracy of estimating the general mean when constructing a confidence interval in the case of a known general variance?
7. What determines the accuracy of estimating the general mean when constructing a confidence interval in the case of an unknown general variance?
8. What determines the number of degrees of freedom in Student's distribution?
9. An estimate of the regression coefficient at x of the two-dimensional linear regression equation Y for X is found by the formula:
10. The pairwise correlation coefficient between variables is -1.
11. The pair correlation coefficient between variables is 1. This means:
12. Throw a dice. Find the probability of getting a face with 1 or 3 points:
13. Throw a dice. Find the probability of getting a face with 6 points:
14. Throw a dice. Find the probability of getting a face with an odd number of points:
15. Throw a dice. Find the probability of getting a face with an even number of points:
16. In tasks for calculating the probability that in n independent trials event A will appear from a to b times, it is used with a large number of trials and probability p different from 0 and 1:
17. In problems for calculating the probability that in n independent trials the event A will appear exactly m times, it is used with a large number of trials and a small probability p:
18. In tasks for calculating the probability that in n independent trials event A will appear exactly m times, it is used with a large number of trials and probability p different from 0 and 1:
19. What are the limits of the probability of occurrence of a random event?
20. Within what limits does the multiple coefficient of determination change?
21. Within what limits does the multiple correlation coefficient change?
22. Within what limits does the pair correlation coefficient change?
23. Within what limits does the partial correlation coefficient change?
24. Which of these concepts of combinatorics includes all elements of the set under study?
25. In what criterion is the G-distribution used?
26. In what criterion is the normal distribution used?
27. What criterion uses the Pearson distribution?
28. What criterion uses Student's distribution?
29. What criterion uses the Fischer-Snedekor distribution?
30. There are 12 standard and 3 defective parts in a box. Take out 1 item. Find the probability that this part is standard.
31. There are 12 standard and 3 defective parts in a box. Take out 1 item. Find the probability that this part is defective.
32. There are 4 standard and 2 defective parts in a box. Two parts are taken out in a row, while not returning them back to the box. Find the probability that both parts taken out are defective.
33. There are 4 standard and 2 defective parts in a box. Two parts are taken out one by one, and each time they are returned back to the box. Find the probability that both parts taken out are defective.
34. In a bunch of 10 similar keys from safes. Determine the probability with which the first randomly selected keys can open a safe with two sequentially opening locks.
35. In the theory of statistical evaluation, estimates are:
36. There are 2 white and 3 black balls in an urn. Take out the ball. Find the probability that this ball is white
37. There are 2 white and 3 black balls in an urn. Two balls are drawn in a row, and each time the balls are returned back to the basket. Find the probability that both balls drawn are white.
38. There are 2 white and 3 black balls in an urn. Two balls are taken out in a row, while the balls are not returned back to the basket. Find the probability of
Additional Information
40. The sample is representative. It means that:41. A sampling set (sample) is a set of results selected from the general population:
42. Hyperbolic with respect to the argument, the regression equation has the form:
43. The boundaries of the two-sided critical region at a given significance level α are found from the relation:
44. The boundaries of the left-hand critical region for a given significance level α are found from the relation:
45. The boundaries of the right-handed critical region at a given significance level α are found from the relation:
46. Two events are called incompatible (incompatible) if:
47. Two events are called joint (compatible) if:
48. What hypothesis is used to test statistics
49. If in the three-dimensional set XYZ it turned out that the pair coefficient between X and Y is greater in absolute value than the quotient, and the coefficients do not have different signs, then this means:
50. If in the three-dimensional set XYZ it turned out that the pair coefficient between X and Y is less than the quotient in absolute value, and the coefficients do not have different signs, then this means:
51. If the probability of the occurrence of one event depends on whether another event occurred, then they are called:
52. If the probability of the occurrence of one event does not depend on whether another event occurred, then they are called:
53. If all values of a random variable are increased by a certain number of times, how will its variance change?
54. If all values of a random variable are increased by a certain number of times, how will its mathematical expectation change?
55. If all values of a random variable are increased by some number, how will its variance change?
56. If all values of a random variable are increased by some number, how will its mathematical expectation change?
57. If all values of a random variable are reduced by a certain number of times, how will its variance change?
58. If all values of a random variable are reduced by a certain number of times, how will its mathematical expectation change?
59. If all values of a random variable are reduced by some number, how will its variance change?
60. If all values of a random variable are reduced by some number, how will its mathematical expectation change?
61. If two events can happen at the same time, then they are called:
62. If two events cannot occur simultaneously, then they are called:
63. If the mathematical expectation of the estimate for any sample size is equal to the most estimated parameter, then the point estimate is called:
64. If the null hypothesis is rejected as a result of testing the criterion, what is the probability of making an error?
65. If a random variable is distributed according to the normal law, then its arithmetic mean is distributed:
66. If an event may or may not occur as a result of a test, then it is called:
67. If an event does not occur during any test, then it is called:
68. If an event necessarily occurs at each test, then it is called:
69. If a point estimate of a parameter with an increase in the sample size converges in probability to the most estimated parameter, then the point estimate is called:
70. The significance of the regression equation is checked using statistics that have a distribution:
71. From a deck of 36 cards, one is drawn at random. What is the probability that it will be a queen of diamonds?
72. From a deck of 36 cards, one card is drawn at random. What is the probability that it will be a lady?
73. From a deck of 36 cards, one is drawn at random. What is the probability that it will be a card of diamonds?
74. From a deck of 52 cards, one is drawn at random. What is the probability that it will be the jack of spades?
75. From a deck of 52 cards, one card is drawn at random. What is the probability that it will be a jack?
76. From a deck of 52 cards, one card is drawn at random. What is the probability that it will be a card of spades?
77. From a deck of 52 cards, one card is drawn at random. What is the probability that it will be a card of hearts?
78. From a deck of 52 cards, one card is drawn at random. What is the probability that it will be the king of spades?
79. From a deck of 52 random cards