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stats help plz ASAP

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Suppose that one of every 100 people ina certain community is infected with HIV. You want to identify an HIV-positive person ina study of an experimental new drug. How many individuals would you expect to have to interview in order to find the first person who is HIV-positive?

I have to see if this is a geometeric distribution or not. For it to be a geometric, the rules are:

1) each observation fall into one of just 2 categories, which for convienience we call "success" or failure."
2) All observations are independent
3) the probabilipt of a success is the same for each observation.
4) The variable of interest is the number of trials required to obtain the first success.

My answer: I think the answer is no it is not a geometric distribution because the probability changes everytime. If the first person picked is HIV negative, then the probability for the second person is different because there's one less person.


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