Discrete Mathematics

Discrete Random Variables

Discrete Random Variables - Indicator Variables

         

The fine when caught speeding by a speed camera is 9090 dollars, and that when caught running a red light is 160160 dollars. If caught doing both at the same time, then the fine is twice the sum of the penalties of doing each. If D2iD_{2i} and D3iD_{3i} denote the indicator variables of speeding and running a red light, respectively, which of the following correctly represents the fine yiy_i (in dollars) the driver has to pay?

Suppose that the average initial monthly salary (in 10410^4 KRW) of a company employee in South Korea is given by the formula: yi=104+94D2i+162D3i+210D4i,y_i=104+94D_{2i}+162D_{3i}+210D_{4i}, where the default is educated up to high school, and D2i,D3i,D_{2i}, D_{3i}, and D4iD_{4i} are the indicator variables for having a bachelor's degree, master's degree, and PhD, respectively. What is the expected salary difference (in 10410^4 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 66 dollars for the first hour, and costs an additional fee of 55 dollars for every additional hour. There is also an extra charge of 1010 dollars for trucks, while compact cars get a 50% discount. If the random variable XX represents the number of hours parked, and D2iD_{2i} and D3iD_{3i} denote the indicator variables for trucks and compact cars, respectively, which of the following represents the equation for the parking fee YiY_i (in dollars)?

Note: XX 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.X=3.

Suppose that the remaining life expectancy (in months) when diagnosed with lung cancer is given by the formula: yi=5411D2i29D3i47D4i,y_i=54-11D_{2i}-29D_{3i}-47D_{4i}, where D2i,D3i,D_{2i}, D_{3i}, and D4iD_{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: yi=157D2i8D3i,y_i=15-7D_{2i}-8D_{3i}, where D2iD_{2i} and D3iD_{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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