In a new promotional activity at Starbucks, whenever you buy a coffee, they give you fortune cookie, on which there is the digit 1,2, or 3, i.e., one of them. So whenever, you buy a coffee, you look at the number and if it is a number that you do not have it, then you collect that number. When you collect the numbers 1, 2, and 3, then Starbucks gives you a free coffee. (a) (10 Pts.) If X represents the number of coffees you need to purchase in order to get a free coffee, determine PMF of X for X values only until 5. No need to get the PMF for the other values of X since there will be two many cases. (b) (10 Pts.) As we can see in Part a, the PMF calculation will be too hectic for the next values of X. Hence, the calculation for the parameters like mean and variance would be difficult. However, we can determine the mean of this distribution by using the concept of geometric distribution. After modeling your problem at hand with geometric distribution, determine how many coffees you need to purchase to get a free coffee?