Your firm operates two divisions of equal size. As a risk manager for the firm you have been collecting claims data on each division. You are able to calculate that the variance of claims for Division A is $25$ and the variance of claims for Division B is $36.$ You have also calculated the covariance between the claims of the two divisions. The covariance is $18.$

$($a$)$ What is the correlation coefficient of the claims for the two divisions?

$($b$)$ What is the standard deviation of the firm$$s claims?

$($c$)$ Is the objective risk of the firm lower or higher than the objective risk of its divisions?