Let X = the time between two successive arrivals at the drive-up window of a loc

Question

Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with = 1, (which is identical to a standard gamma distribution with = 1), compute the following. (If necessary, round your answer to three decimal places.)

(a) The expected time between two successive arrivals


(b) The standard deviation of the time between successive arrivals


(c)    P(X 3)


(d)    P(2 X 5)

You may need to use the appropriate table in the Appendix of Tables

Explanation / Answer

from exponential distribution:

a)  expected time between two successive arrivals =1/ =1

b)  standard deviation of the time between successive arrivals =1/ =1

c) P(X<=3) =1-e-t =1-e-1*3 =0.9502

d)P(2<=X<=5) =(1-e-1*5)-(1-e-1*2 ) =0.1353-0.0067 =0.1286

please revert for any clarification required,

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