The number of messages that arrive at a Web site is a Poisso

The number of messages that arrive at a Web site is a Poisson distributed random variable with a mean of 6 messages per hour. Round your answers to four decimal places. What is the probability that 5 messages are received in 1 hour? What is the probability that 10 messages are received in 1.5 hours? What is the probability that less than 2 messages are received in 1/2 hour?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X = 5 ) = e ^-6 * 6^5 / 5! = 0.1606
b)
Per hours the rate of passengers are 6
Per 1 hour 30 minutes it is 9
P( X = 10 ) = e ^-9 * 9^10 / 10! = 0.1186
c)
Per hours the rate of passengers are 6
Per 30 min the mean rate of passengers be 3
P( X < 2) = P(X=1) + P(X=0)
= e^-3 * 10 ^ 1 / 1! + e^-3 * ^ 0 / 0!
= 0.1991