Calculating the variance and standard deviation: Kate recentlyinvested in realestate with the intention of selling the property one year fromtoday. She hasmodeled the returns on that investment based on three economicscenarios. Shebelieves that if the economy stays healthy then her investmentwill generate a30 percent return. However if the economy softens as predictedthe returnwill be 10 percent while the return will be 25 percent if theeconomy slipsinto a recession. If the probabilities of the healthy soft andrecessionarystates are 0.4 0.5 and 0.1 respectively then what are theexpected returnand the standard deviation for Kates investment?