Expected return and standard deviation $($S$7\mathrm{.}2)$ A game of chance offers the following

odds and payoffs. Each play of the game costs $$100,$ so the net profit per play is the payoff

less $$100.$

Year Nominal Return $(\%)$ Inflation $(\%)$

$201541\mathrm{.}410\mathrm{.}7$

$201666\mathrm{.}26\mathrm{.}3$

$201726\mathrm{.}92\mathrm{.}9$

$201815\mathrm{.}02\mathrm{.}7$

$201932\mathrm{.}63\mathrm{.}7$

$20202\mathrm{.}13\mathrm{.}7$

What are the expected cash payoff and expected rate of return? Calculate the variance and

standard deviation of this rate of return. $($Do not make the adjustment for degrees of freedom

described in footnote $12.)$