Question

The number of tickets issued by a meter reader for parking-meter violations can be modeled by a Poisson process with a rate parameter of five per hour. What is the probability that exactly three tickets are given out during a particular hour? Find the mean and standard deviation of this distribution.

P(X=3) = 0.1404

Mean = 5

Standard deviation = 2.2361

UNANSWERED: What is the probability that exactly 10 tickets are given out during a particular 3-hour period?

Answer 1

X ~ Poi ( )

Where = 5 per hour .

Poisson probability distribution is

P(X) = e^- * ^X / X!

a)

P(X = 3) = e^-5 * 5³ / 3!

= 0.1404

b)

Mean = = 5

c)

Standard deviation = Sqrt ()

= sqrt(5)

= 2.2361

d)

For 3 hour period , = 3 * 5 = 15

P(X = 10) = e^-15 * 15¹⁰ / 10!

= 0.0486