exercise:657eb04de7: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Suppose we are attending a college which has 3000 students. We wish to choose a subset of size 100 from the student body. Let <math>X</math> represent the subset, chosen using the following possible strategies. For which strategies would it be...") |
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Suppose we are attending a college which has 3000 students. We wish to choose a subset of size 100 from the student body. Let <math>X</math> represent the subset, chosen using the following possible strategies. For which strategies would it | |||
We wish to choose a subset of size 100 from the student body. Let <math>X</math> represent the | |||
subset, chosen using the following possible strategies. For which strategies would it | |||
be appropriate to assign the uniform distribution to <math>X</math>? If it is appropriate, what | be appropriate to assign the uniform distribution to <math>X</math>? If it is appropriate, what | ||
probability should we assign to each outcome? | probability should we assign to each outcome? | ||
<ul><li> Take the first 100 students who enter the cafeteria to eat lunch. | <ul style="list-style-type:lower-alpha"><li> Take the first 100 students who enter the cafeteria to eat lunch. | ||
</li> | </li> | ||
<li> Ask the Registrar to sort the students by their Social Security number, and then | <li> Ask the Registrar to sort the students by their Social Security number, and then | ||
Latest revision as of 00:00, 14 June 2024
Suppose we are attending a college which has 3000 students. We wish to choose a subset of size 100 from the student body. Let [math]X[/math] represent the subset, chosen using the following possible strategies. For which strategies would it be appropriate to assign the uniform distribution to [math]X[/math]? If it is appropriate, what probability should we assign to each outcome?
- Take the first 100 students who enter the cafeteria to eat lunch.
- Ask the Registrar to sort the students by their Social Security number, and then take the first 100 in the resulting list.
- Ask the Registrar for a set of cards, with each card containing the name of exactly one student, and with each student appearing on exactly one card. Throw the cards out of a third-story window, then walk outside and pick up the first 100 cards that you find.