2.4: An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is 0.3.

2.4.1 Use both the Geometric and Negative Binomial probability distribution functions to calculate the probability that the third hole drilled is the first to yield a productive well? (3)

2.4.2 If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well? Use the Binomial and Geometric distributions to calculate the probability and appropriately interpret your answer.

2.5 We observe a sequence of independent identical trials with two possible outcomes on

each trial, and , and with () = . The number of the trial on which we observe the fifth success, has a negative binomial distribution with parameters = 7 and . Suppose that we observe the fifth success on trial number 12.

2.5.1 Find the value of p that maximizes ( = 12).

2.5.2 Generalize the result from part (2.5.1) to find the value of that maximizes

( = 0) when has a negative binomial distribution with parameters (known) and .