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.
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