Statistics probability questions

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Homework Help Overview

The discussion revolves around a probability problem involving a Poisson distribution related to the number of exercises prepared by Stéphane each week. The problem includes multiple parts that require calculating probabilities based on different scenarios, including the arrival of a visiting scholar and the expected number of exercises assigned.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the application of the Poisson distribution and conditional probability to solve the problem. There is an exploration of drawing probability trees to visualize the scenarios presented in the questions. Some participants express uncertainty about the correct interpretation of expected values and the implications of the problem's wording.

Discussion Status

Some participants have made progress on parts of the problem, particularly part b, and have shared their calculations. However, there remains uncertainty regarding part c, with participants questioning the expected values and the interpretation of the problem's context. Guidance has been offered regarding the use of probability trees and the need for clarity in the problem statement.

Contextual Notes

There are noted ambiguities in the problem's wording, particularly regarding the timing of the exercises and the implications of the last week of the semester. Participants are considering different interpretations of the scenario, which may affect their calculations.

  • #31
Ray Vickson said:
It makes perfectly good sense to ask for the posterior probability of a visiting scholar, given that a student answered 3 questions correctly and without making any assumption that the test has 5 questions. Admittedly the problem is more challenging than the "assume 5 questions" version, and may possibly be beyond the ability/knowledge of the OP, but I really do not know what the instructor intended, so having two possible versions cannot hurt...

First of all, if 3 questions are answered correctly the test must contain ##N \geq 3## questions.$$

I think your response is fair and you are definitely right that the wording is open for multiple interpretations. In my book, having an observation is a very big deal and the wording is silent whether or not the student has even received the assignment... all we have to go on is, that the student "is expected to answer 3 questions correctly." It seems to me that clarity is important generally in math and especially so in probability, but this question is not clear.

That said, maybe OP's prof meant to write a good homework question, but was interrupted by a visitor from Switzerland.
 

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