The mean vector is $[3\mathrm{.}33,2\mathrm{.}5,4\mathrm{.}6]$

and the covariance matrix is

$[(4\mathrm{.}22,-3\mathrm{.}67,2\mathrm{.}36),$

$(-3\mathrm{.}67,3\mathrm{.}58,-1\mathrm{.}55),$

$(2\mathrm{.}36,-1\mathrm{.}55,5\mathrm{.}25)]$

a$.$ Based on the above information, what is the mean of 'Score$3\text{'}?$

b$.$ What is the variance of 'Score$2\text{'}?$

c$.$ What is the covariance between 'Score$1\text{'}$ and 'Score$2\text{'}?$

d$.$ Based on the sign and magnitude of the covariance between 'Score$1\text{'}$ and 'Score$2\text{'},$ what observations can you make?

e$.$ Compute the correlation between 'Score$1\text{'}$ and 'Score$2\text{'}$ using the values in the covariance matrix.

f$.$ Based on the sign and magnitude of the correlation between 'Score$1\text{'}$ and 'Score$2\text{'},$ what observations can you make?