Variance and standard deviation $($expected$).$ 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: $$ The probability of a boom economy is $10\%,$ the probability of a stable growth economy is $19\%,$ the probability of a stagnant economy is $47\%,$ and the probability of a recession is $24\%.$ 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.

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