If a Poisson random variable X has an average of 2.6, find: p(X<2).
To find P(X<2), we first need to find the probability mass function for the Poisson random variable X with an average of 2.6.
The probability mass function for a Poisson random variable X with an average of λ is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Given that the average λ = 2.6, we can calculate the probability of X being less than 2 as follows:
P(X < 2) = P(X = 0) + P(X = 1)
P(X = 0) = (e^(-2.6) * 2.6^0) / 0! = e^(-2.6) ≈ 0.073
P(X = 1) = (e^(-2.6) * 2.6^1) / 1! = 2.6e^(-2.6) ≈ 0.191
Therefore, P(X < 2) = 0.073 + 0.191 ≈ 0.264
Thus, the probability that a Poisson random variable X with an average of 2.6 is less than 2 is approximately 0.264.