I am not pushing religion on anybody I also am not going to be negative to your thoughts but I am going to state my claim The bible tells us that Jesus is the same yesterday today and forever he fails not and he loves forever no matter your mistakes or faults he gives you strength when you are weak and comfort when you are down never give up on him because he has never given up on you never stop loving him because he has never stopped loving you never lose faith because he has never lost faith in you never doubt the one who has never doubted you when you are going through hell keep going because if you give up, you stop, and hell is no place to stop so keep going because it is the trials that make you stronger

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.