If a Poisson random variable X has an average of 2.6 find: p(X=3)
A)0.4256
B)0.3256
C)0.2176
D)0.1864
E)0.1126
Using the Poisson probability formula, we have:
P(X = x) = (e^(-λ) * λ^x) / x!
Where λ is the average of the Poisson random variable.
In this case, λ = 2.6 and x = 3:
P(X = 3) = (e^(-2.6) * 2.6^3) / 3!
P(X = 3) = (0.0723 * 17.576) / 6
P(X = 3) = 1.268026 / 6
P(X = 3) = 0.2113377
Therefore, the closest answer choice is C) 0.2176