If a Poisson random variable X has an average of 2.6 find:
4.2
3.8
3.5
2.6
2.1
To find the probability that X is equal to a specific value, we can use the Poisson probability formula: P(X = x) = (e^(-λ) * λ^x) / x!
Given that the average (λ) for the Poisson random variable X is 2.6, we can calculate the probabilities for the specified values:
1. P(X = 4.2): This is not a valid integer value for a Poisson random variable, so the probability would be 0.
2. P(X = 3.8): Also not a valid integer value, so the probability would be 0.
3. P(X = 3.5): Again, not a valid integer value, so the probability would be 0.
4. P(X = 2.6): This is the average value of the Poisson random variable, so the probability would be: P(X = 2.6) = (e^(-2.6) * 2.6^(2.6)) / 2.6! ≈ 0.177842
5. P(X = 2.1): This is another valid integer value for X, so the probability would be: P(X = 2.1) = (e^(-2.6) * 2.6^(2.1)) / 2.1! ≈ 0.207651
Therefore, the probabilities for the specified values are:
P(X = 4.2) = 0
P(X = 3.8) = 0
P(X = 3.5) = 0
P(X = 2.6) ≈ 0.177842
P(X = 2.1) ≈ 0.207651