Statistics?

Question

It is known that an outbreak of this type of infestation occurs , on the average , every 30 years .Assuming that this phenomenon obeys an exponential probability law, what is the probability that catastropheic outbreaks of spruce budworn infestation will occur within 6 years of each other.

Answer 1

The exponential probability law has the probability density function
p(x) = kexp(-kx)
and the probability distribution function
D(x) = P(X< or =x) = 1 - exp(-kx)
where p(x) = D'(x) and D(0) =0.
The mean is
= 1/k

In your problem
= 1/k = 30
k = 1/30
P(X< or =6) = 1 - exp(-6/30) = 0.18127...