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 yes because the probability is the same for each observation which 1/100. the trials are independent and there is success of getting HIV and not getting a HIV patient
right?
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Yes, you are correct. In this scenario, all the conditions for a geometric distribution are satisfied.
1) Each individual can be classified as either HIV-positive (success) or not HIV-positive (failure).
2) Each interview is independent of the others because the probability of finding an HIV-positive person does not depend on previous interviews.
3) The probability of finding an HIV-positive person is the same for each interview, as it is stated that one out of every 100 people in the community is infected with HIV.
4) The variable of interest is the number of interviews required until the first success (finding the first HIV-positive person).
To calculate how many individuals you would need to interview to find the first HIV-positive person, you can use the formula for the expected value (mean) of a geometric distribution, which is given by 1/p, where p is the probability of success.
In this case, p is 1/100 since the probability of finding an HIV-positive person is 1 out of 100. Therefore, you would expect to interview 1/(1/100) = 100 individuals on average before finding the first HIV-positive person.
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