Assume that the probability of each elementary event {i} defined in the sample space = {1,

Assume that the probability of each elementary event {i} defined in the sample space Ω = {1, 2, 3,…} is given by P({i}) = 5i−1∕7i, i = 1, 2, 3,….

Let us define the events An = {n, n + 1, n + 2, n + 3, n + 4}, n = 1, 2, 3,….

(i) After establishing that the relationship

holds, verify that limn→∞P(An) = 0.
(ii) Can you use the result of Proposition 1.11 to conclude that

Transcribed Image Text:

P(A) = = (-)" n-1 P P(A), n=1,2,3,....