If a Poisson random variable X has an average of 2.6, find: p(X greater than equal to 5)
To find P(X >= 5), we can use the Poisson probability formula:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the average, which is 2.6 in this case.
P(X >= 5) = 1 - P(X < 5)
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= (e^(-2.6) * 2.6^0) / 0! + (e^(-2.6) * 2.6^1) / 1! + (e^(-2.6) * 2.6^2) / 2! + (e^(-2.6) * 2.6^3) / 3! + (e^(-2.6) * 2.6^4) / 4!
= (e^(-2.6) * 1) + (e^(-2.6) * 2.6) + (e^(-2.6) * 6.76) + (e^(-2.6) * 17.576) + (e^(-2.6) * 45.6976)
= 0.0724 + 0.1880 + 0.3666 + 0.4600 + 0.5167
= 1.6037
Therefore, P(X >= 5) = 1 - 1.6037 = 0.3963
So, the probability that X is greater than or equal to 5 is 0.3963.