Thread: you

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 don’t know the probability p of missing a bus. You miss the bus 13 times during
the year. You estimate p by the sample mean, pˆ . What are the mean and variance of the sample
mean?

Originally Posted by sadasoria

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 don’t know the probability p of missing a bus. You miss the bus 13 times during
the year. You estimate p by the sample mean, pˆ . What are the mean and variance of the sample
mean?

Well you didn't post any work, and didn't say what you were having trouble with, so I'll just make a few comments.

a) Do we know the total number of days? The point of this question, I think, is that often the expected value is an impossible value, e.g., it's not possible to have 2.5 children. So quite possibly the probability is 0.

b and c) Consult your book for formulas, or look on Wikipedia.

If you have any specific questions, ask away.

Also, please try to pick a more descriptive title (instead of "you") next time.