Question

We consider the experiment of picking a point at random from the interval (0, 1). The sample space for this experiment is the interval (0, 1). We consider three sequences of events in this sample space En = ( 1 n , 1) Fn = (1 − 1 n , 1), Gn = ( 1 2 − 1 2n , 1 − 1 2n ), n positive integer. (a) Is (En) ∞ n=1 increasing, decreasing, both, or neither? (b) Is limn→∞ En defined? If so, what is it (express your answer in interval notation). (c) Is (Fn) ∞ n=1 increasing, decreasing, both, or neither? (d) Is limn→∞ Fn defined? If so, what is it (express your answer in interval notation). (e) Is (Gn) ∞ n=1 increasing, decreasing, both, or neither? (f) Is limn→∞ Gn defined? If so, what is it (express your answer in interval notation).

Answer 1