Question

Among the most famous of all meteor showers are the Perseids, which occur each year in early August. In some areas the frequency of visible Perseids can be as high as 40 per hour. What is the probability that an observer who has just seen a meteor will have to wait at least 5 minutes before seen another.

Answer 1

the required probability is 0.0357

Explanation:

Given the data in the question;

X-Exp( λ = 40/60 = 0.6667

Pdf: f( x ) = λe^(-λx), 0 < x

so

Cdf: P( X < x ) = 1 - e^(-λe)

( X ≤ x ) = 1 - e^(-λe), for x > 0 ⇒ p( X > x ) = e^(-λe)

now to wait at least 5 minutes before seen another

p(X > 5 ) = e^(-λe)

we substitute

p(X > 5 ) = e^(-0.6667 × 5)

p(X > 5 ) = e^(-3.3335)

p(X > 5 ) = 0.035668 ≈ 0.0357

Therefore, the required probability is 0.0357