If a Poisson random variable X has an average of 2.6 find:
0.4686
0.6546
0.5246
0.3894
0.3454
To find these probabilities, we need to use the Poisson probability formula:
P(X = k) = (e^(-λ) * λ^k) / k!
Where:
- λ is the average rate (in this case, 2.6)
- k is the particular value we are interested in
For the values provided:
1. P(X = 2) = (e^(-2.6) * 2.6^2) / 2! = 0.4686
2. P(X = 3) = (e^(-2.6) * 2.6^3) / 3! = 0.6546
3. P(X = 4) = (e^(-2.6) * 2.6^4) / 4! = 0.5246
4. P(X = 1) = (e^(-2.6) * 2.6^1) / 1! = 0.3894
5. P(X = 0) = (e^(-2.6) * 2.6^0) / 0! = 0.3454