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?
Probability Mass Function of X following Poisson Distribution with mean = 2.5 is given by:
for x = 0, 1,..
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
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