Suppose the research shows that there are three possible economics scenarios in 2023: Recession, stagnation and slow growth with the probability 0.6, 0.3 and 0.1. There are three investment opportunities with the rate of return (R1,R2,R3) as follows: Suppose we allocate an investment with following weight w1=20%,w2=40%,w3=40% Problem 1: Find the portfolio rate of return for each economic scenario. Problem 2: Find the expected rate of return and the variance for the portfolio: p=E[Rp],p2=Var(Rp). You must submit each problem in a separate page. Suppose the research shows that there are three possible economics scenarios in 2023: Recession, stagnation and slow growth with the probability 0.6, 0.3 and 0.1. There are three investment opportunities with the rate of return (R1,R2,R3) as follows: Suppose we allocate an investment with following weight w1=20%,w2=40%,w3=40% Problem 1: Find the portfolio rate of return for each economic scenario. Problem 2: Find the expected rate of return and the variance for the portfolio: p=E[Rp],p2=Var(Rp). You must submit each problem in a separate page