If a Poisson random variable X has an average of 2.6 find: p(X=3)

Answer 1

To find the probability of X being equal to 3, we can use the Poisson probability mass function formula:

P(X = k) = (e^(-λ) * λ^k) / k!

where:
- λ is the average number of events that occur in a fixed interval (in this case, 2.6)
- k is the specific number of events we are interested in (in this case, 3)

Plugging in the values, we get:

P(X = 3) = (e^(-2.6) * 2.6^3) / 3!

Calculating the expression, we find:

P(X = 3) ≈ 0.222

Therefore, the probability of X being equal to 3 in this case is approximately 0.222.