If a Poisson random variable X has an average of 2.6 find:
0.4256
0.3256
0.2176
0.1864
0.1126
To find these values, we need to use the Poisson probability formula:
P(X = x) = (e^(-λ) * λ^x) / x!
where λ is the average (2.6 in this case) and x is the observed value. Let's calculate each of the probabilities:
1. P(X = 0):
P(X = 0) = (e^(-2.6) * 2.6^0) / 0! = e^(-2.6) ≈ 0.0727
2. P(X = 1):
P(X = 1) = (e^(-2.6) * 2.6^1) / 1! = 2.6 * e^(-2.6) ≈ 0.1897
3. P(X = 2):
P(X = 2) = (e^(-2.6) * 2.6^2) / 2! = 2.6^2 * e^(-2.6) / 2 ≈ 0.3293
4. P(X = 3):
P(X = 3) = (e^(-2.6) * 2.6^3) / 3! = 2.6^3 * e^(-2.6) / 6 ≈ 0.3612
5. P(X = 4):
P(X = 4) = (e^(-2.6) * 2.6^4) / 4! = 2.6^4 * e^(-2.6) / 24 ≈ 0.2813
Therefore, the probabilities matching the given values are:
- 0.4256 : Not matched
- 0.3256 : Not matched
- 0.2176 : Not matched
- 0.1864 : Not matched
- 0.1126 : Not matched