Question

Let the mean success rate of a Poisson process be 8 successes per hour.

Let the mean success rate of a Poisson process be 8 successes per hour. a. Find the expected number of successes in a 33 minutes period. (Round your answer to 4 decimal places.) Expected number of successes b. Find the probability of at least 2 successes in a given 33 minutes period. (Round your answer to 4 decimal places.) Probability c. Find the expected number of successes in a two hours period. (Round your answer to 2 decimal places.) Expected number of successes d. Find the probability of 16 successes in a given two hours period. (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability

Answer 1

X ~ Poi($\lambda$)

Where $\lambda$ = 8 per hour.

a)

For 33 minutes,

$\lambda$ = 8 * 33 / 60 = 4.4

E(X) = 4.4

b)

P(X ) = e^-$\lambda$*$\lambda$^X / X!

P(X >= 2) = 1 - P(X <= 1)

= 1 - [ P(X = 0) + P(X = 1) ]

= 1 - [ e^-4.4 + e^-4.4 * 4.4 ]

= 0.9337

c)

For 2 hour period,

$\lambda$ = 2 * 8 = 16

E(X) = 16

d)

P(X = 16) = e^-16 * 16¹⁶ / 16!

= 0.0992