Suppose an oil prospector will drill a succession of holes in a given area until he nd a productive well. The number of attempts it takes to nd the rst productive well can be modeled as a random variable that follows a geometric distribution. Let X be the random variable that denotes number of attempts it takes to nd the rst productive well. Let p represent the probability that the prospector is successful on a given trail. For instance, if the fourth well drilled is the rst productive well1 then [61 = 4 will be the single observation for the random variable X. We observe an oil prospectors attempt this scenario, each time recording the number of attempts until they nd a productive well. This scenario can be represented by X1, X2, . , X\" be an iid random sample from a geometric distribution with e, p) 2 p(1 p)_1 with 0