You take a bus to school everyday. The probability that you miss the bus is p = 0.05
independent of other days.
a) What is the probability that the number of busses you miss is equal to the expected value of the
number of busses you miss?
b) Upon you miss a buss you take a taxi and pay 10 TL or 12 TL with probabilities 0.3 and 0.7,
respectively. Find the mean and variance of the money you pay to taxies in a year.
c) Suppose you donít know the probability p of missing a bus. You miss the bus 13 times during
the year. You estimate p by the sample mean, pą . What are the mean and variance of the sample