If a Poisson random variable X has an average of 2.6 find P(X greater or =4)
To find P(X greater or equal to 4) for a Poisson random variable with an average of 2.6, we use the Poisson probability mass function:
P(X = k) = (e^(-λ) * λ^k) / k!
Where λ is the average parameter of the Poisson distribution, and k is the value we are interested in (in this case, 4).
First, we need to calculate the probability of X being less than 4.
P(X < 4) = 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!
Now, calculate each of these probabilities:
P(X < 4) = (0.07 + 0.18 + 0.24 + 0.26)
P(X < 4) = 0.75
Since the sum of all probabilities must equal 1, we can find P(X >= 4) by subtracting P(X < 4) from 1:
P(X >= 4) = 1 - P(X < 4)
P(X >= 4) = 1 - 0.75
P(X >= 4) = 0.25
Therefore, P(X greater or equal to 4) for a Poisson random variable with an average of 2.6 is 0.25.