Question

An oil company has 10 offshore rigs scattered throughout a wide area in the Gulf of Mexico. Officials feel that under normal operating conditions, each rig has only a 1% chance of having an oil spill during the year.

1. Define the random variable X. Explain carefully the distribution.

2. Find the expression of the probability mass function.

3. Compute the expected value E(X), the variance V ar(X) and standard deviation _.

4. If the rigs were located close together and some unusual situation ocurred (such as a hurricance or an earthquake), it is safe to assume that X was binomial? Explain.

Answer 1

(1) X is a Binomial random variable denoting the number of successes in a binomial experiment. In this case, it is denoting the number of offshore oil rigs that may suffer an oil spill during the year.
The distribution is used to describe a Binomial experiment, which contains:
(i) a fixed number of trials,
(ii) there are 2 possible outcomes in this experiment - oil spill (success) or no oil spill (failure),
(iii) the probability of success, p = 0.01, remains the same in every trial, and
(iv) the trials are independent.

(b)

(c) , ,


(d) If the rigs had been located close to each other and there was some unusual weather conditions, then it would have not been safe to assume X to be binomial. This is due to the fact that the trails (in this case, oil rigs) would not have been independent. Since the oil rigs are situated close to each other, mutliple oil rigs could have suffered oil spills. Hence, the condition of the binomial experiment would have been violated. Thus, in that case, assuming X to be binomial would not have been safe.