Question

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?

Answer 1

X ~ Poisson( $\lambda$ )

Where $\lambda$ = 2.1

P(X) = e^{- $\lambda$} $\lambda$ ^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