Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time is 2.5, then P(x = 0) is:

A) 2.5
B) 0.0821
C) 1.5811
D) 0.40
E) 1

Question

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time is 2.5, then P(x = 0)  is:A)  2.5B)  0.0821C)  1.5811D)  0.40E)  1

Mardrika Webster · Accepted Answer

Final Answer : B, Explanation :  Using the Poisson formula, P(x = k) = (λ^k * e^(-λ)) / k!, where λ is the average number of events and k is the specific number of events we want to find the probability of.In this case, λ = 2.5 and k = 0, so P(x = 0) = (2.5^0 * e^(-2.5)) / 0! = 0.0821.

Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time is 2.5, then P(x = 0) is:

A) 2.5
B) 0.0821
C) 1.5811
D) 0.40
E) 1

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