Probability
# Discrete Random Variables

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.