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 the probability density function given by

()={ y, 0< <1

2, 1 < 2

0, }

a. Find the CDF F(y).

b. Find the probability that the station will pump between 8000 and 12000 gallons in a particular month.