Читать книгу Probability and Statistical Inference - Robert Bartoszynski - Страница 54

1 2.3.1 Label all statements below as true or false. (i) If is more likely to occur than , then . (ii) If occurs whenever does, then . (iii) If then whenever occurs, does also. (iv) If , then must occur three times out of every four. (v) The sum of probabilities of disjoint events and cannot exceed 1. (vi) If and are not disjoint, the sum of their probabilities exceeds 1. (vii) If and are all positive, then is also positive. (viii) If sample spaces for two experiments are identical, then the probability of the same event must be the same for both experiments.

2 2.3.2 A bathroom floor is covered by square tiles with side length . You drop a coin with diameter , where . Find: (i) The probability that the coin will rest entirely within one tile. (ii) The probability that the coin will partially cover four different tiles.

3 2.3.3 Show that first and third, as well as second and third, schemes of sampling chords (see Bertrand's paradox) are not equivalent.