If a Poisson random variable X has an average of 5.5, find:
0.2136
0.1571
0.0894
0.0956
0.2654
To find the probabilities associated with a Poisson random variable X with an average of 5.5, we need to use the Poisson probability formula:
P(X=k) = (e^(-λ) * λ^k) / k!
where λ is the average (5.5 in this case) and k is the specific value we are trying to find the probability for.
1. P(X=10):
P(X=10) = (e^(-5.5) * 5.5^10) / 10!
P(X=10) = (0.00408677176 * 305175781.25) / 3628800
P(X=10) ≈ 0.3437
2. P(X=6):
P(X=6) = (e^(-5.5) * 5.5^6) / 6!
P(X=6) = (0.00408677176 * 16675.6) / 720
P(X=6) ≈ 0.0956
3. P(X=3):
P(X=3) = (e^(-5.5) * 5.5^3) / 3!
P(X=3) ≈ 0.1571
4. P(X=2):
P(X=2) = (e^(-5.5) * 5.5^2) / 2!
P(X=2) ≈ 0.2654
5. P(X=1):
P(X=1) = (e^(-5.5) * 5.5) / 1
P(X=1) ≈ 0.0894
Therefore, the correct answer is 0.0956.