Fill in the spaces your correct answers. The decimal 0.7 is the sum of an infinite geometric series with first term and common ratio D As a ratio of two integers in lowest terms, 0.7 = ajo 0 (0) 0 15
EXERCISES
1.2.1 Suppose S = {1, 2, 3), with P({1})= 1/2, P({2})= 1/3, and P({3)) = 1/6. (a) What is P({1, 2})? (b) What is P({1,2,3})? (c) List all events A such that P(A) = 1/2.
1.2.2 Suppose S = (1, 2, 3, 4, 5, 6, 7, 8), with P({s})= 1/8 for 1 < s < 8. (a) What is P({1, 2})? (b) What is P({1, 2, 3])? (c) How many events A are there such that P(A) = 1/2?
1.2.3 Suppose S (1, 2, 3), with P({1}) = 1/2 and P((1, 2)) = 2/3. What must. P({2}) be?
1.2.4 Suppose S = (1, 2, 3), and we try to define P by P({1, 2, 3)) = 1, P({1,2)) = 0.7, P(1, 3)) = 0.5, P({2,3}) = 0.7, P((1)) = 0.2. P((2)) = 0.5, P({3)) = 0.3. Is P a valid probability measure? Why or why not?
