Problem $2.$ This problem takes you through the formal definition of risk aversion $/$ risk

loving. Given a lottery P$,$ let E $($P$)$ be the expected value of the lottery P$.$ For example, if

P $=($$$10,0\mathrm{.}5$; $$0,0\mathrm{.}5),$ then

E $($P$)=0\mathrm{.}5\backslash$times $10+0\mathrm{.}5\backslash$times $0=5$

We say a person is

$$ Risk averse if he chooses E $($P$)$ dollars for sure over the lottery P

$$ Risk neutral if he is indifferent between E $($P$)$ dollars and the lottery P

$$ Risk loving if he chooses the lottery P over E $($P$)$ dollars for sure.