Discrete Mathematics

# Discrete Random Variables - Indicator Variables

The fine when caught speeding by a speed camera is $$90$$ dollars, and that when caught running a red light is $$160$$ dollars. If caught doing both at the same time, then the fine is twice the sum of the penalties of doing each. If $$D_{2i}$$ and $$D_{3i}$$ denote the indicator variables of speeding and running a red light, respectively, which of the following correctly represents the fine $$y_i$$ (in dollars) the driver has to pay?

Suppose that the average initial monthly salary (in $$10^4$$ KRW) of a company employee in South Korea is given by the formula: $y_i=104+94D_{2i}+162D_{3i}+210D_{4i},$ where the default is educated up to high school, and $$D_{2i}, D_{3i},$$ and $$D_{4i}$$ are the indicator variables for having a bachelor's degree, master's degree, and PhD, respectively. What is the expected salary difference (in $$10^4$$ KRW) between Roger who has a PhD and Cliff who has a bachelor's degree?

Suppose there is a parking lot where the parking fee is $$6$$ dollars for the first hour, and costs an additional fee of $$5$$ dollars for every additional hour. There is also an extra charge of $$10$$ dollars for trucks, while compact cars get a 50% discount. If the random variable $$X$$ represents the number of hours parked, and $$D_{2i}$$ and $$D_{3i}$$ denote the indicator variables for trucks and compact cars, respectively, which of the following represents the equation for the parking fee $$Y_i$$ (in dollars)?

Note: $$X$$ is calculated as the smallest integer that is larger or equal to the actual number of hours parked. For instance, if a car is parked for 2 and half hours, then $$X=3.$$

Suppose that the remaining life expectancy (in months) when diagnosed with lung cancer is given by the formula: $y_i=54-11D_{2i}-29D_{3i}-47D_{4i},$ where $$D_{2i}, D_{3i},$$ and $$D_{4i}$$ are the indicator variables for stages 2, 3, and 4, respectively. If Ronald is diagnosed with lung cancer stage 3, how many more months is he expected to live?

Note: There are four stages in lung cancer, where increasing stage results in worse prognosis.

The entrance fee (in dollars) of a museum is given by the formula: $y_i=15-7D_{2i}-8D_{3i},$ where $$D_{2i}$$ and $$D_{3i}$$ are the indicator variables for children (under 15 years of age) and the handicapped, respectively. What is the entrance fee for a 12-year-old handicapped child?

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