If a Poisson random variable X has an average of 2.6 find:P(X greater or =5)
A)0,3112
B)0,2876
C)0,2133
D)0,1889
E)0,1226
To find P(X greater or equal to 5) with an average of 2.6 using the Poisson distribution formula, we can calculate it as follows:
P(X ≥ 5) = 1 - P(X < 5) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)
Using the Poisson distribution formula P(X = x) = (e^(-λ) * λ^x) / x! where λ is the average rate, which in this case is 2.6, and x is the value we are interested in:
P(X = 0) = (e^(-2.6) * 2.6^0) / 0! = e^(-2.6)
P(X = 1) = (e^(-2.6) * 2.6^1) / 1! = 2.6 * e^(-2.6)
P(X = 2) = (e^(-2.6) * 2.6^2) / 2! = (2.6^2 / 2) * e^(-2.6)
P(X = 3) = (e^(-2.6) * 2.6^3) / 3! = (2.6^3 / 6) * e^(-2.6)
P(X = 4) = (e^(-2.6) * 2.6^4) / 4! = (2.6^4 / 24) * e^(-2.6)
Now, we can substitute these values back into the equation to find P(X ≥ 5):
P(X ≥ 5) = 1 - e^(-2.6) - 2.6 * e^(-2.6) - (2.6^2 / 2) * e^(-2.6) - (2.6^3 / 6) * e^(-2.6) - (2.6^4 / 24) * e^(-2.6)
Calculating this expression gives approximately 0.3112
Therefore, the answer is:
A) 0.3112