Question

The number of hits to a web site follows a Poisson distribution.  If the average number of hits per minute is 6, answer the following questions:

The probability of no hits in the next minute?

The probability of exactly eight hits in the next minute?

The probability of exactly eight hits in the next 2 minutes?

The probability of at least 6 hits in the next 2 minutes?

Expected number of hits in an hour?

Answer 1

Here, lambda =6 per minute

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

a)

P(x = 0) = e^6 * 6^0/0!
= 0.0025

b)

P(x = 8) = e^6 *6^8/8!
= 0.1033

c)

Here, lambda = 12

P(x= 8) = e^12*12^8/8!
= 0.0655

d)

P(x>=6) = 1 - P(x< =5)
= 1 - P(x=0) - P(x=1) -...... - P(x=5)
= 1 - e^12 * 12^0/0! - e^12 * 12^1/1! - ..... - e^12 * 12^5/5!

= 0.9797

e)

Expected number in hour = 6 * 60 = 360