# Practice Exam - Question #6 - Discrete Distributions

Hi team,

Thanks for your hard work! Great material.

I do not understand why the solution to this problem is not simply 3 + 8. The way it's worded, it seems like the answer should be 3 + 8. Claude, the AI tool, also thought the answer should be 11.

Please clarify this for me. Thanks!

Here's what

**Claude**said when I provided it the solution to the problem:*I apologize, but there appears to be an error in the explanation provided in the image. The explanation is incorrect and inconsistent with the principles of the Poisson distribution.*

*In a Poisson distribution with parameter λ, the mean (expected value) is equal to λ. Therefore:*

*For family cars with λ = 3, the mean is 3, not 1/3.*

*For single-member cars with λ = 8, the mean is 8, not 1/8.*

*The correct solution should be:*

*Mean of family cars: 3 Mean of single-member cars: 8 Sum of means: 3 + 8 = 11*

*The explanation in the image incorrectly inverts the λ values, which is not mathematically valid for Poisson distributions. The sum should indeed be 11, but it's obtained by adding 3 and 8 directly, not by adding their reciprocals.*

*This mistake in the explanation likely caused your confusion. You were correct in your earlier reasoning when you added 3 and 8 to get 11. That is the correct approach for finding the sum of the expected values (means) of these two Poisson distributions.*

1 answers ( 0 marked as helpful)

Hey Justin,

Thank you for bringing this to our attention! The question is now replaced.

Let us know if you encounter other issues.

Kind regards,

365 Hristina