Calculation of variance and standard deviation.
Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on the investment based on three economics scenarios. She believes that if the economy stays healty, then her investment will generate a 30 percent retuen. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be - 25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4,0.5, and 0.1, respectively, then what are the expected return and the standard deviation of the return on Kate's investment?