Question

Consider a Poisson distribution with .a. Select the appropriate Poisson probability function.

1) P(x; λ) = (e⁻λ * λˣ) / x!
2) P(x; λ) = (e⁻λ * λˣ) / (x-1)!
3) P(x; λ) = (e⁻λ * λˣ) / (x+1)!
4) P(x; λ) = (e⁻λ * λˣ) / (x+2)!

Answer 1

The correct Poisson probability function that describes the number of events occurring in a fixed interval with a known average rate and independently of time since the last event is P(x; λ) = (e^−λ * λ^x) / x!.The correct option is 2.

Step-by-step explanation:

The student is trying to identify the correct Poisson probability function from a list of options. The Poisson distribution describes the probability of a number of events occurring in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event. When X follows a Poisson distribution with a mean (μ or λ), the correct probability function is:

P(x; λ) = (e−λ * λx) / x!

The formula includes a factor of e raised to the power of the negative mean (e−λ), multiplied by the mean to the power of the number of occurrences (x), and this product is then divided by the factorial of the number of occurrences (x!). Therefore, the correct option is:

1. P(x; λ) = (e−λ * λx) / x!