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?

Question

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.

right?

Answer 1

Yes, you are correct. In this scenario, it is not a geometric distribution because the probability of finding an HIV-positive person changes with each interview. The probability is not the same for each observation, as it depends on the number of HIV-positive individuals in the community at the particular moment. Since the probability changes after each interview, it does not meet the criteria for a geometric distribution.