Statistics and ProbabilitySuppose we are making $25 per hour. We are told by someone that if we meet with him betweenthe hours 0 and 4 he will hand us $X. However we do not know exactly when this person will be at the meeting place. All we know is that his arrival time is equal likely from Hour 0 to Hour 4, and he will leave immediately if he does not find us waiting at the meeting point. If we arrive at the meeting point after Hour 0 we will not know if this person has already left or is yet to show up. Under this setting, we are to decide when to go to the meeting point (t) and how much to wait (w). During w, we do not have any hourly income and as such, we lose $25 for each hour we spend waiting for this person. Assuming that the travel times to and from the waiting times are negligible, compute our optimal arrival time (t*) and wait time (w*) as functions of X that will maximize our total income.