Using the conditional probability formula

Solved Step by Step With Explanation- P(X=2) & P(X=2|X≤3) Probability

Questions

(b) What is P(X=2∣X≤3) ?

Answer

In this case, k = 2 and λ = 5. So, you have:

P(X=2) = (e^(-5) * 5^2) / 2!

First, find the probabilities for X=0, X=1, X=2, and X=3:

P(X=0) = (e^(-5) * 5^0) / 0! = e^(-5) / 1 = e^(-5)

P(X≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

P(X≤3) = e^(-5) + 5 * e^(-5) + 0.08447 + (125/6) * e^(-5)

P(X=2 | X≤3) = 0.08447 / [(1 + 5 + 0.08447 + 125/6) * e^(-5)]

P(X=2 | X≤3) ≈ 0.0151