suppose your expectations regarding the stock price and holding period return $($hpr$)$ are as follows: boom $0\mathrm{.}2$ probability, $$60$ end price, $38\mathrm{.}6\%$ hpr$,$ normal growth $0\mathrm{.}5$ probability, $$50$ end price, $13\mathrm{.}2\%$ hpr$,$ recession $0\mathrm{.}3$ probability, $$30$ end price, $-18\mathrm{.}4\%$ hpr$.$ compute the mean and standard deviation of the hpr on the stock. also what is the real return on the stock if the inflation rate is $2\mathrm{.}9\%.$