A stock is expected to return $16\%$ in a normal economy, return $24\%$ if the economy booms, and lose $13\%$ if the economy moves into a recessionary period. Economists predict a $65\%$ chance of a normal economy, a $25\%$ chance of a boom, and a $10\%$ chance of a recession. What is the expected return on the stock?

Over the past $3$ years an investment returned $21\mathrm{.}25\%,-15\mathrm{.}25\%,$ and $18\mathrm{.}25\%.$ What is the variance of returns?

Over the past $4$ years an investment returned $20\mathrm{.}0\%,-11\mathrm{.}0\%,-14\mathrm{.}0\%,$ and $17\mathrm{.}0\%.$ What is the standard deviation of returns?

Calculate the variance of returns for Alpha stock with the following historical rates of return:

$2018$:$20\mathrm{.}36\%$

$2019$:$25\mathrm{.}24\%$

$2020$:$30\mathrm{.}24\%$

What is the standard deviation of returns of a portfolio that produced returns of $10\mathrm{.}44\%,15\mathrm{.}88\%,26\mathrm{.}32\%,$ and $30\mathrm{.}44\%?$