In a very large population that has a proportion of a particular disease p, a researcher conducting a study on this disease, is taking samples sequentially until she receives three cases consecutively. find the mean and the variance of the number of samples she needs to take.

2）conduct a simulation of 1000 runs for p=0.6 to compute the empirical values for the mean and the variance and compare your empirical results with the results using the formulas in (1).