Question

2. The number of times a geyser erupts in one day follows a Poisson distribution with mean 2.5. On a randomly selected day:

   (a) what is the probability that there are no eruptions? (b) what is the probability of at least 3 eruptions?

Answer 1

(a)

Probability Mass Function of X following Poisson Distribution with mean = 2.5 is given by:

,

            for x = 0, 1,..

So,

Answer is:

0.0821

(b)

P(X3) = 1 - [P(X=0) + P(X=1)+P(X=2)]

Substituting, we get:

P(X3) = 1 - [P(X=0) + P(X=1)+P(X=2)] = 1 - 0.5438 = 0.4562

So,

Answer is:

0.4562