At his workplace, the first thing Oscar does every morning is to go to the supply room and pick up one, two, or three pens with equal probability 1/3....

At his workplace, the first thing Oscar does every morning is to goto the supply room and pick up one, two, or three pens with equal probability 1/3. Ifhe picks up three pens, he does not return to the supply room again that day. If hepicks up one or two pens, he will make one additional trip to the supply room, wherehe again will pick up one, two, or three pens with equal probability 1/3. (The numberof pens taken in one trip will not affect the number of pens taken in any other trip.)Calculate the following:(a) The probability that Oscar gets a total of three pens on any particular day.(b) The conditional probability that he visited the supply room twice on a given day,given that it is a day in which he got a total of three pens.(c) E[N] and E[N |C], where E[N] is the unconditional expectation of N, the totalnumber of pens Oscar gets on any given day, and E[N |C] is the conditionalexpectation of N given the event C = {N >3}.(d) σN |C, the conditional standard deviation of the total number of pens Oscar getson a particular day, where N and C are as in part (c).(e) The probability that he gets more than three pens on each of the next 16 days.(f) The conditional standard deviation of the total number of pens he gets in thenext 16 days given that he gets more than three pens on each of those days.