If a Poisson random variable X has an average of 2.6 find: p(1 < X < 4).
To find P(1 < X < 4) 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, which in this case is 2.6.
First, we need to find the individual probabilities for each value in the range (1 < X < 4):
P(X = 2) = (e^(-2.6) * 2.6^2) / 2! = (0.0747 * 6.76) / 2 = 0.2535
P(X = 3) = (e^(-2.6) * 2.6^3) / 3! = (0.0747 * 17.576) / 6 = 0.2233
Then we sum the probabilities for each value to get the total probability within the range:
p(1 < X < 4) = P(X= 2) + P(X= 3) = 0.2535 + 0.2233 = 0.4768
Therefore, the probability of getting a value between 1 and 4 for a Poisson random variable with an average of 2.6 is 0.4768.