If a Poisson random variable X has an average of 2.6 find:P(X greater or =5)
To find P(X greater or equal to 5) for a Poisson random variable with an average of 2.6, we can use the Poisson probability formula:
P(X = k) = (e^(-λ) * λ^k) / k!
Where λ is the average rate of occurrence. In this case, λ = 2.6.
Now we need to calculate P(X = 5) and then add the probabilities for all values greater than or equal to 5.
P(X = 5) = (e^(-2.6) * 2.6^5) / 5!
= (0.0732 * 148.877256) / 120
= 0.0901
Now, to find P(X >= 5), we need to sum the probabilities for X = 5, X = 6, X = 7, and so on.
P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + ...
≈ 0.0901 + 0.0819 + 0.0565 + ...
You can continue this calculation to find the exact value, or you can use a statistical software or calculator to find the cumulative probability quickly.