Discuss the below:
Q1. A baseball team loses $10,000 foe each Consecutive day it rains. Say X,the number of consecutive days it rains at the beginning of the season has a Poisson ditatibution with mean 0.2. What is the expected loss before the opening game?
Q2. An airline always overbooks if possible. A part ular plane has 95 seats on a Eight in which a 44 sells for $300.The airline sells 100 such ticketski this flight.
(a) if the probability of an individual not showing up is OM assuming independence, 44 is the probability that the airline can accomodate all the passengers who do show up?
(b) If the airline must return the $300 price plus a penalty of $103 to each passenger that cannot get on the flight, what is the expand payout (penalty plus ticket refund) that tie airline will pay?
Q3. Assume that a policyholder it four times more likely to file exactly two claims as to file exactly three claims. Assume also that the number X of claims of this policyholder is Poisson. Determine the expectation E(X2 ).
Q4. In the decade of the 1980s. the number X of caxses of diphtheria reported each year in the United State; followed a Poisson distribution with men 2.5. Wbat is the probability that
(a) No Wes were reported in a given year?
(b) Exactly thee eases were reported?
(c) At least three cases were reported?