Meteors can be seen in the night sky as shooting stars according to a Poisson process with rate λ = 3 meteors per hour. Suppose you’re watching for meteors, and you see each one with probability p = 0.4, independently of all others. Say whether each of the following statements is true or false, showing any working.

a. The probability that there are 2 meteors in an hour is 3 2

2! e

−3

.

b. The probability that there are no meteors in an hour is e

−3

.

c. The probability that a meteor occurs in any interval of 20 minutes is 1 − e

−1

.

d. The probability that you see five of the first ten meteors is 10 5

(0.4)

5

(0.6)

5

.

e. The probability that it takes longer than half an hour before a meteor appears is e

−3/2

.