Chapter 4.2, Problem 14E

A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. The total amount of gas pumped at the station in a month is a random variable Y (measured in 10,000 gallons) with a probability density function given by

$f\left(y\right)=\{\begin{array}{l}y,0\text{ < }y<1,\\ \text{2-}y\text{, 1}\le y<2,\\ 0,\text{ elsewhere}\text{.}\end{array}$

1. a Graph f(y).
2. b Find F(y) and graph it.
3. c Find the probability that the station will pump between 8000 and 12,000 gallons in a particular month.
4. d Given that the station pumped more than 10,000 gallons in a particular month, find the probability that the station pumped more than 15,000 gallons during the month.