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Landings at an airport are exponentially distributed with a mean of 1 plane per hour.

a) What is the probability that more than 3 airplanes land within an hour?

b) If 15 separate 1 hour intervals are chosen, what is the probability that no interval contains more than 3 landings.

c) What is the probability that exactly 2 planes land in 2 hours.

d) What is the probability that the waiting period for 3 arrivals will be more than 3 hours?

f) What is the mean and variance for the waiting time for 3 arrivals?

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So I tried to solve this and failed. I started by getting the exponential distribution function:

e^(-x) which didn't give me the answer to a) so I turned towards the general expression:

e^(-1) / x!

This gave me an answer 0.019 that does not make sense...can someone be kind enough to walk me through this exercise? I would offer $ via paypal but I think the forum doesn't allow it...lmk

Ty!