Hull$$ Consultants, a famous think tank in the$$ Midwest, has provided probability estimates for the four potential economic states for the coming year in the following$$ table: LOADING.... The probability of a boom economy is $15\%,$ the probability of a stable growth economy is $20\%,$ the probability of a stagnant economy is $52\%,$ and the probability of a recession is $13\%.$ Calculate the variance and the standard deviation of the three$$ investments: stock, corporate$$ bond, and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are$$ correct, which investment would you$$ choose, considering both risk and$$ return?$$

$$Hint: Make sure to round all intermediate calculations to at least seven$(7)$ decimal places. The input$$ instructions, phrases in parenthesis after each answer$$ box, only apply for the answers you will type.