Question

# The number of times a geyser erupts in one day follows a Poisson distribution with mean...

1. 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?

(a)

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

for x = 0, 1,.. So,

0.0821

(b)

P(X 3) = 1 - [P(X=0) + P(X=1)+P(X=2)]   Substituting, we get:

P(X 3) = 1 - [P(X=0) + P(X=1)+P(X=2)] = 1 - 0.5438 = 0.4562

So,

0.4562

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