Assume that the number of new visitors to a website in one hour is distributed as a Poisson random variable. The mean number of new visitors to the website is 2.1 per hour. Complete parts (a) through (d) below.
-What is the probability that in any given hour exactly one new visitor will arrive at the website?
-What is the probability that in any given hour two or more new visitors will arrive at the website?
-What is the probability that in any given hour fewer than three new visitors will arrive at the website?
X ~ Poisson( )
Where = 2.1
P(X) = e-X / X!
a)
P( X = 1) = e-2.1 *2.1
= 0.2572
b)
P (X >= 2) = 1 - P( X <= 1)
= 1 - [ P (X = 0) + P (X = 1) ]
= 1 - [ e-2.1+ e-2.1 *2.1]
= 0.6204
c)
P( X < 3) = P (X <= 2)
= P (X = 0) + (X + 1 ) + P (X = 2)
= e-2.1+ e-2.1 *2.1 + e-2.1 2.12 / 2!
= 0.6496
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