Financial Risk Manager Part 1

Explanation

For a Poisson random variable:

• E(X) = λ = 0.25
• The probability mass function is: P(X=k) = (e^(-λ) * λ^k) / k!

For P(X=1): P(X=1) = (e^(-0.25) * (0.25)^1) / 1! = e^(-0.25) * 0.25

Calculating: e^(-0.25) ≈ 0.7788 0.7788 * 0.25 ≈ 0.1947 ≈ 0.19

Therefore, P(X=1) = 0.19, which matches option C.