Question

If the average number of occurrences for a Poisson process is 2 occurrences per five minute time interval, the probability of getting 2 occurrences over a five minute interval is _______.

a. 0.3233 b. 0.2707 c. 0.6767 d. 0.8038 e. 0.1822

Answer 1

Solution :

Given that ,

mean = = 2

Using poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

P(X 2) = 1 − P( X 2)

P(X 2) = 1 - ( P(X = 0) + P(X = 1) + P(X = 2))

P(X 2) = 1 - ( (e^-2 * 2⁰⁾ / 0! +  (e^-2 * 2¹⁾ /1! +  (e^-2 * 2²⁾ / 2!)

P(X 2) = 1 - 0.6767

P(X 2) = 0.3233

Probability = 0.3233

Option a is correct.

The answer is 0.3233