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In: Advanced Math

In a chaotic world far far away, a professor notices that his students begin to miss...

In a chaotic world far far away, a professor notices that his students begin to miss classes randomly- they either show up or not with no preference. So he decides to take attendance. There are a total of eight classes in the semester. He knows that if he takes attendance each time, he will have an absolutely accurate measurement of his students' overall attendance rate (6/8, 7/8 etc). But he gets lazy and wants to take attendance every other class (his students don't know about this). Now each attendance counts for two: if a student shows up in 3 of the 4 times the professor takes attendance, he gets an overall attendance rate of 6/8. In this case, what is the professor's measurement error of a student's actual attendance rate? What if the professor take attendance only twice (each counts for four)? What if he only takes attendance once (counts for eight)?

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