Statistics Question

Question

The average number of radioactive particles passing through a counter during 1 millisecond in a lab experiment is 13. Find the probability that more than 4 milliseconds pass between particles.

Answer 1

The timing of radioactive decay is an example of the exponential distribution with the distribution parameter lambda (λ)

λ = 1/ average event rate = 1/13 = 0.291 per millisecone

Using the cumulative exponential distribution the probability of a time between decays being 4 or more milliseconds is

P(X > x) = e^-xλ or e^-(4·.291) or .312