A ski resort operator must decide before the winter season whether he will lease a snow-making machine. If he has no machine, he will make $20,000 if the winter is mild, $30,000 if it is typical, and $50,000 if the winter is severe. If he decides to lease the machine, his profits for these conditions will be $30,000, $35,000, and $40,000, respectively. The probability of a mild winter is 0.3, with a 0.5 chance of a typical winter and a 0.2 chance of a severe winter. If the operator wants to maximize his expected profit, should he lease the machine? What is the most he should be willing to pay for a perfect forecast?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A ski resort operator must decide before the winter season whether he will lease a snow-making machine.
If he has no machine, he will make $20,000 if the winter is mild, $30,000 if it is typical, and $50,000 if the winter is severe. If he decides to lease the machine, his profits for these conditions will be $30,000, $35,000, and $40,000, respectively. The probability of a mild winter is 0.3, with a 0.5 chance of a typical winter and a 0.2 chance of a severe winter.
If the operator wants to maximize his expected profit, should he lease the machine? What is the most he should be willing to pay for a perfect
forecast?
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