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?
This does fit your definition of "a geometric."
I hope this helps. Thanks for asking.
Yes, you are correct. In this scenario, the number of individuals you would expect to have to interview in order to find the first person who is HIV-positive follows a geometric distribution.
Each interview can be considered a trial, and the probability of success (finding an HIV-positive person) is the same for each trial, which is 1/100 since one out of every 100 people in the community is infected with HIV. The trials (interviews) are also independent because the outcome of one interview does not affect the outcome of another.
Therefore, the variable of interest is the number of trials (interviews) required to obtain the first success (finding an HIV-positive person), which fits the definition of a geometric distribution.
To calculate the expected number of interviews, you can use the formula for the expected value of a geometric distribution, which is given by 1/p, where p is the probability of success. In this case, p = 1/100. So, the expected number of interviews would be 1/(1/100) = 100.
Hence, you would expect to have to interview approximately 100 individuals in order to find the first person who is HIV-positive.