The stocks A and B have the following distributions of returns.

A B Probability

State $1340\mathrm{.}2$

State $2520\mathrm{.}3$

State $3480\mathrm{.}2$

State $4650\mathrm{.}1$

State $5610\mathrm{.}2$

$($i$)$ What are the means, variances and standard deviations of stocks A and B$?$

$($ii$)$ What are the covariance and correlation between stocks A and B$?$

$($iii$)$ Consider a portfolio with $=0\mathrm{.}50$ in A and $1-=0\mathrm{.}5$ in B$.$ What are the mean,

variance and standard deviation of this portfolio?