$3-$For the three problems $($a$,$ b$,$ and c$)$ below: $(2$ Points$)$

Consider historical data showing that the average annual rate of return on the S&P $500$ portfolio over the past $90$ years has averaged roughly $8\%$ more than the Treasury bill return, and that the S&P $500$ standard deviation has been about $20\%$ per year. Assume these values are representative of investors' expectations for future performance and that the current T$-$bill rate is $5\%.$

a$.$ Calculate the expected return and variance of portfolios invested in T$-$bills and the S&P $500$ index with weights as follows:

$\backslash$table$[[W_{\text{b}\text{i}\text{l}\text{l}\text{s}},W_{\text{i}\text{n}\text{d}\text{e}\text{x}}$