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1. Let X and Y be independent discrete random variables, X having the geometric distribution with parameter p and Y having the geometric distribution with parameter r. What is the distribution of min{X, Y}?

2. You arrive at the opening of a new cafe, which has only two chairs. Unfortunately, there are three people ahead of you in the line. You know that the number of minutes that a guest spends in a cafe is a geometric random variable with mean 2, and that the time each guest spends in the cafe is independent of all other guests. What is the probability that you will have to wait strictly more than n minutes.