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

Question

Quizplus · Accepted Answer

The probability mass function for a Poisson random variable is given by P(X=k) = (e^-λ * λ^k) / k!, where λ is the expected value of X. Here, λ=2.5 and we want to find P(X=0). 
P(X=0) = (e^-2.5 * 2.5^0) / 0! = e^-2.5 ≈ 0.0821 (using a calculator or the approximation e^-x ≈ 1-x when x is small). Therefore, the best choice is (B).

Given a Poisson Random Variable X,where the Average Number of Times