An engineer is participating in a research project on the title patterns of junk

Question

An engineer is participating in a research project on the title patterns of junk emails. The number of junk emails which arrive in an individual's account every hour follows a Poisson distribution with a mean of 1.9. (a) What is the expected number of junk emails that an individual receves in an 12-hour day? (b) What is the probability that an Individual receives more than two junk emalls for the next three hours? Round your answer to two decimal places (e.g. 98.76) (C) What is the probability that an individual receives no junk email for two hours? Round your answer to three decimal places (e.g. 98.765).

Explanation / Answer

Poisson's Distribution Formula:
P(X = x) = (e^-) (^x) / x!

a)
here 1-hour lambda = 1.9 mails per hour
For 12 hours, expected number of junk emails = 1.9*12 = 22.8

b)
For 3 hours, lambda = 1.9*3 = 5.7
P(X>2) = 1 - P(X<=2)
= 1 - P(X=0) - P(X=1) - P(X=2)
= 1 - e^-5.7 - e^-5.7*5.7 - e^-5.7*5.7^2/2
= 0.92

c)
For two hours, lambda = 1.9*2 = 3.8
P(X=0) = e^-3.8 = 0.02

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