The number of hits to a Web site follows a Poisson process. Hits occur at the rate of 0.9 per minute between 7:00 P.M. and 10:00
P.M. Given below are three scenarios for the number of hits to the Web site. Compute the probability of each scenario between 8:12 P.M.
and 8:21 P.M.
(a) exactly four.
(b) fewer than four.
(c) at least four.
Given Hits occur at the rate of 0.9 per minute
Between 8:12 P.M and 8:21 P.M we have 9 minutes
λ = 0.9 * 9 = 8.1
(a) exactly four
P(X = K) = (e^-λ * λ^k)/k!
P(X = 4) = (e^-8.1 * 8.1^4)/4! = 0.05444
(b) fewer than four.
P(X = K) = (e^-λ * λ^k)/k!
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) +P(X = 3) = 0.03961
or Excel : POISSON.DIST(3,8.1,TRUE) = 0.039605
(c) at least four
P(X >= 4) = 1 - P(X < 4) = 1-0.03961 = 0.96039
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