Exercise $5-27$ Algo

Investment advisors recommend risk reduction through international diversification. International investing allows you to take advantage of the potential for growth in foreign economies, particularly in emerging markets. Janice Wong is considering investment in either Europe or Asia. She has studied these markets and believes that both markets will be influenced by the U$.$S$.$ economy, which has a $21\%$ chance for being good, a $52\%$ chance for being fair, and a $27\%$ chance for being poor. Probability distributions of the returns for these markets are given in the accompanying table.

State of the U$.$S$.$ Economy Returns in Europe Returns in Asia

Good $10\%24\%$

Fair $4\%4\%$

Poor $3\%18\%$

a$.$ Find the expected value and the standard deviation of returns in Europe and Asia. $($Round intermediate calculations to at least $4$ decimal places and final answers to $2$ decimal places.$)$