If a Poisson random variable X has an average of 8.8, find: p(X is greater or equal to 2)

Answer 1

To find this probability, we will use the Poisson probability formula:

P(X = k) = (e^(-λ) * λ^k) / k!

where λ is the average rate of occurrences per unit time or space.

Given that the average of X is 8.8, λ = 8.8.

Now, we want to find P(X ≥ 2), which is equal to 1 - P(X < 2).

P(X < 2) = P(X = 0) + P(X = 1)

P(X = 0) = (e^(-8.8) * 8.8^0) / 0! = e^(-8.8)
P(X = 1) = (e^(-8.8) * 8.8^1) / 1! = 8.8e^(-8.8)

Therefore,
P(X < 2) = e^(-8.8) + 8.8e^(-8.8)

P(X ≥ 2) = 1 - P(X < 2) = 1 - (e^(-8.8) + 8.8e^(-8.8))

Calculating the value of the above expression will give you the final probability.