Question

2. Suppose that the number X of takeoffs at a certain airport which are Airbus is...

2. Suppose that the number X of takeoffs at a certain airport which are Airbus is recorded. Assume that X has a binomial distribution with p = 0.35 are Airbus and that the number of takeoffs in a day is 200

a) Form a probability distribution approximated by Poisson for the number takeoffs (0-200) by Airbus in one day

b) Draw a histogram.

c) Find the expected value.

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Answer #1

Here, n is large, so doing Poisson approximation for binomial distribution, we get

mean = n*p = 0.35*200 = 70

a) Hence, if X is the number of Airbus takeoffs during a day, we have

P(X=k) = =

b) The histogram for the probability distribution (X-axis is no. of takeoffs, Y-axis is probability):

c) Expected value = rate parameter = 70

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