If a Poisson random variable X has an average of 2.6 find:P(X greater or =4)
A)0.6452
B)0.7125
C)0.7566
D)0.8774
E)0.8126
To find P(X greater or equal to 4), we can use the Poisson probability formula:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the average rate of success, in this case, 2.6.
P(X greater or equal to 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
P(X greater or equal to 4) = 1 - (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!
P(X greater or equal to 4) = 1 - (0.0735 + 0.1910 + 0.2493 + 0.2166)
P(X greater or equal to 4) ≈ 1 - 0.7304
P(X greater or equal to 4) ≈ 0.2696
Therefore, the answer is not listed above. The correct probability is approximately 0.2696.