Suppose X_1 is an observation for Bob, X_5 is an observation for Alice, X_7 is an observation for Charlie.

Question

Using the following facts about Bob:

P( -2 < X_1 < 2 ) \approx 0.95 \quad \text {and} \quad P(-\sqrt[5]{2} \le X_1 \le \sqrt[5]{2}) \approx 0.75,

compute the probability

P( -2 < X_5 < 2, \; -2 < (X_7)^5 < 2)

of an event involving Alice and Charlie?

(Enter the probability P( -2 < X_5 < 2, \; -2 < (X_7)^5 < 2) or if the probability is not determined uniquely, then enter -1.)

(Enter a numerical answer accurate to at least 3 decimal places.)

P( -2 < X_5 < 2, \; -2 < (X_7)^5 < 2)=

Answer 1

Since the problem only provides information about Bob and not about Alice or Charlie, we cannot directly determine the probability of the event involving Alice and Charlie. Therefore, the probability is not determined uniquely, and the answer is -1.