MH8131 Probability and Statistics Assignment

Reference no: EM132603253

MH8131 Probability and Statistics - Nanyang Technological University

(1) Suppose that of all individuals buying a certain digital camera, 60% include an optional memory card in their purchase, 40% include an extra battery, and 30% include both a card and battery. Consider randomly selecting a buyer and

A = memory card purchased, B = battery purchased.
(a) Find probabilities P (A) and P (B).

(b) Given that the selected individual purchased an extra battery, what is the probability that an optional card was also purchased ?
(c) Given that the selected individual purchased an optional card, what is the probability that an extra battery was also purchased ?
(d) Are the events A and B independent ? Justify it.

(2) A company is considering drilling four oil wells. The probability of success for each well is 0.40, independent of the results for any other well. The cost of each well is $200, 000. Each well that is successful will be worth $600,000.
(a) What is the probability that one or more wells will be successful ?
(b) What is the expected number of successes ?
(c) What is the expected gain ?

(3) An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. Their statistics show that an accident-prone person will have an accident at some time within a fixed 1- year period with probability 0.4, whereas this probability decreases to 0.2 for a non-accident -prone person.
• If we assume that 30 percent of the population is accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy ?
• Suppose that a new policyholder has an accident within a year of pur- chasing a policy. What is the probability that he or she is accident prone
?

(4) Investigate the rivers data. The U.S. Geological Survey recorded the lengths (in miles) of several rivers in North America. They are stored in the vector rivers in the datasets package (which ships with base R). Type ?rivers in R console. Plot its histogram and boxplot. Specify the median and 75% quantile and identify whether there are outliers. Include your R codes as well.

Reference no: EM132603253

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