Question

Consider a Poisson distribution with λ = 3. Select the appropriate Poisson probability function.

1) P(x;3) = (e⁻³)(3ˣ)/(x!)
2) P(x;3) = (e⁻³)(3ˣ)
3) P(x;3) = (e⁻³)/(x!)
4) P(x;3) = (3ˣ)/(x!)

Answer 1

The correct Poisson probability function for a distribution with λ = 3 is P(x;3) = (e^-3)(3^x) / (x!).

Step-by-step explanation:

To determine the appropriate Poisson probability function for a distribution with λ = 3, we can recall the general form of the Poisson distribution:

P(X = x; λ) = ​(e-λλx) / (x!)

Considering the options provided:

1. P(x;3) = (e-3)(3x) / (x!) is the correct formula for Poisson distribution where λ equals 3.
2. P(x;3) = (e-3)(3x) is missing the division by x!.
3. P(x;3) = (e-3) / (x!) does not include the term 3x.
4. P(x;3) = (3x) / (x!) is missing the exponential decay factor e-3.

Therefore, the correct Poisson probability function from the given options is the first one:

P(x;3) = (e-3)(3x) / (x!)