Write the following in math notation.

$1.$ The expected return on a stock $x$ is the sum of the return of the asset in the $1^{st}$ state of the economy and the probability of $1^{st}$ state of the economy, the return on the asset in the $2^{nd}$ state of the economy times the probability of the $2$nd state of the economy, and the return

on the asset in the $3^{rd}$ state of the economy times the probability of the $3^{rd}$ state of the economy.

$2.$ Forty$-$five percent of the portfolio $B$ is invested in Walmart Stock and $55\%$ is invested in Tesla Stock.

$3.$ The standard deviation of P&G$\text{'}$s returns is $0\mathrm{.}065.$

$4.$ Write the general equation to calculate the expected return of portfolio $R$ that contains four stocks are all equally weighted.

Apple stock has a $10\%$ chance of a generating a$12\%$ return, a $50\%$ chance of a $3\%$ return, and a $40\%$ chance of a $20\%$ return.

a$.$ What was the general equation that resulted in the following specific equation: $\mathrm{.}1070=\mathrm{.}10(\mathrm{.}12)+\mathrm{.}05(\mathrm{.}03)+\mathrm{.}4(\mathrm{.}20)$

b$.$ What was the general equation that resulted from the following specific equation: $1\mathrm{.}0=\mathrm{.}10+\mathrm{.}50+\mathrm{.}40$