Without any passengers, an aeroplane has a mass of 4200 kg. The plane has capacity to carry 120 passengers, and when there are 40 passengers on the plane, the total mass of the plane and passenger is 7480 kg. a) calculate the mean mass of passenger b) Hence, write an expression for un that gives the total mass of the plane and passengers when there are n passengers on board c) state the values of n for which your model is valid

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.