HW$3($from Chapter $5)$: Market Return Scenarios for the National Economy In reality, there is a continuum of possible returns. The assumption of only five possible returns is clearly an approximation to reality, but such an approximation is often us$$ful$.$

An investor is concerned with the market return for the coming year, where the market return is defined as the percentage gain $($or loss, if negative$)$ over the year. Th investor believes there are five possible scenarios for the national economy in the coming year: rapid expansion, moderate expansion, no growth, moderate contraction and serious contraction. Furthermore, she has used all of the information available to her to estimate that the market returns for these scenarios are, respectively, $23\%,18\%,15\%,9\%,$ and $3\%.$ That is$,$ the possible returns vary from a high of $23\%$ to a low of $3\%.$ Also, she has assessed that the probabilities of these outcomes are $0\mathrm{.}12,0\mathrm{.}40,0\mathrm{.}25,0\mathrm{.}15,$ and $0\mathrm{.}08.$ Use this information to describe the probability distribution of the market return.