Question

Assume a Poisson distribution.

A). If λ=2.5 P(X =5):P(X=5)is approximately 0.0668.
B) If λ=8.0, find P(X=8):
P(X=8) is approximately 0.0571.
C) If λ=0.5 P(X =2):P(X=2)is approximately 0.0821
D) If λ=3.7 P(X =2):P(X=3)is approximately 0.0999

Answer 1

The Poisson distribution is used to describe the number of events that occur in a fixed interval of time or space. To calculate the probability of a specific number of events occurring, we use the formula P(X = k) = (e^(-λ) * λ^(k)) / k!. We can apply this formula to calculate the probabilities in the given question.

Step-by-step explanation:

In the given question, we are dealing with the Poisson distribution. The Poisson distribution is used to describe the number of events that occur in a fixed interval of time or space. It is especially useful when dealing with rare events, such as accidents or phone calls.

To calculate the probability of a specific number of events occurring, we use the formula P(X = k) = (e^(-λ) * λ^(k)) / k!, where λ is the mean number of events in the interval and k is the number of events we want to find the probability for.

Using this formula, we can calculate the probabilities for the given values of λ and X as follows:

A) If λ = 2.5 and X = 5, P(X = 5) = (e^(-2.5) * 2.5^(5)) / 5! ≈ 0.0668

B) If λ = 8.0 and X = 8, P(X = 8) = (e^(-8.0) * 8.0^(8)) / 8! ≈ 0.0571

C) If λ = 0.5 and X = 2, P(X = 2) = (e^(-0.5) * 0.5^(2)) / 2! ≈ 0.0821

D) If λ = 3.7 and X = 3, P(X = 3) = (e^(-3.7) * 3.7^(3)) / 3! ≈ 0.0999