If a Poisson random variable X has an average of 7.5, find:
0.0645
0.0745
0.0452
0.0592
0.0412
To find the probability that a Poisson random variable with an average of 7.5 equals a specific value k, we use the Poisson probability formula:
P(X=k) = (e^(-λ) * λ^k) / k!
where λ is the average of the Poisson random variable.
Let's calculate the probabilities for each value:
1. k = 5:
P(X=5) = (e^(-7.5) * 7.5^5) / 5! ≈ 0.0645
2. k = 6:
P(X=6) = (e^(-7.5) * 7.5^6) / 6! ≈ 0.0745
3. k = 7:
P(X=7) = (e^(-7.5) * 7.5^7) / 7! ≈ 0.0452
4. k = 8:
P(X=8) = (e^(-7.5) * 7.5^8) / 8! ≈ 0.0592
5. k = 9:
P(X=9) = (e^(-7.5) * 7.5^9) / 9! ≈ 0.0412
Therefore, the correct answer is 0.0645.