An investor has initial wealth $W=$$$2$ and considers participating in a flipping$-$the$-$coin lottery: $50\%$ chance of winning $$1$ and $50\%$ chance of losing $$1.$ Her preferences are described by the utility function $u(w)=\sqrt[\phantom{2}]{W}.$ Using this information, compute the following:

a$)$ The degree of absolute risk aversion ARA

b$)$ The degree of relative risk aversion RRA

c$)$ The expected value of the lottery E$[$L$]$

d$)$ The variance of the lottery Var$[L]$

e$).$ The expected value of final wealth $E[W]$

f$)$ The utility evaluated at expected final wealth $u(E[W])$

g$)$ The expected utility $E[u(W)]$

h$)$ The certainty equivalent level of wealth $W_{CE}$

i$)$ The Markowitz risk premium $.$