Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
Given a Poisson random variable with (E(X) = .25), calculate (P(X=1)).
Other
Community
NNikitesh
A
0.1
B
0.15
C
0.19
D
0.25
Explanation:
For a Poisson distribution, the expected value E(X) = λ = 0.25. The probability mass function for a Poisson random variable is:
P(X = k) = (e^{-λ} * λ^k) / k!
For k = 1: P(X = 1) = (e^{-0.25} * 0.25^1) / 1! P(X = 1) = e^{-0.25} * 0.25
Calculating e^{-0.25} ≈ 0.7788 Then: 0.7788 * 0.25 ≈ 0.1947 ≈ 0.19
Therefore, the correct answer is 0.19.
Comments
Loading comments...