This problem has a young Billy and an older and smarter Billy.

$($

a

$)$

$$Every morning, rain or shine, young Billy Gates can be found at the entrance to the metro, hawking

copies of

$$

The Morningstar.

$$

$$Demand for newspapers varies from day to day, but Billy

$$

s regular

early morning haul yields him

$2$

$0$

$0$

$$copies$.$ He purchases these copies for $

$1$

$$per paper, and sells

them for $

$1$

$.$

$5$

$0$

$$apiece$.$ Billy goes home at the end of the morning, or earlier if he sells out. He

can return unsold papers to the distributor for $

$0$

$.$

$5$

$0$

$$apiece$.$ From experience, Billy knows that

demand for newspapers on any given morning is uniformly distributed between

$1$

$5$

$0$

$$and

$2$

$5$

$0$

$,$

$$where

each of the possible values

$1$

$5$

$0$

$,$

$1$

$5$

$1$

$,$

$.$

$.$

$.$

$,$

$2$

$5$

$0$

$$is equally likely. What is the expected value of Billy

$$

s

net earnings on any given day?