Let the Random Variable $X$ Represent the Winnings at One Play of Game A

question 60

Essay

Let the random variable $X$ represent the winnings at one play of game A. The mean, $\mu$ , of $X$ is known to be $- \$ 0.42$ and its standard deviation, $\sigma$ , is $\$ 0.27$ . Let the random variable $Y$ represent the winnings at one play of game $B$ . The mean, $\mu$ , of $Y$ is known to be $- \$ 0.42$ and its standard deviation, $\sigma$ , is $\$ 0.20$ . You have decided to play one of these two games just once. At which game are you more likely to make a profit (i.e., to not lose money)? Explain your thinking.