please solve handwritten showing work/formulas. thank you in advance will upvote.

(30 pts) Two portfolios A and B. Their returns across different states of economy are described below: State Return for Portfolio A Return for Portfolio B Probability 30% Boom 20% 30% Vormal 40% 10% 15% Recession 30% -10% -15% a. (15 pts) What is the mean and standard deviation of returns for portfolio A? What is the mean and standard deviation of returns for portfolio B? b. (15 pts) What is the covariance and correlation coefficient between portfolios A and B