Use the frequency and severity distributions given to answer the following questions.

Frequency Distribution

Losses Probability

$0$

$1$

$2$

Mean $=\mathrm{.}5$

Std$.$ Dev. $=\mathrm{.}6742$

Skewness $=1\mathrm{.}009$

Severity Distribution

Mean $-=?$

Std$.$ Dev. $=209\mathrm{.}85$

Skewness $=0\mathrm{.}867$

a$.$ Calculate the mean of the severity distribution.

b$.$ Determine the total loss distribution. Show all of the possible losses and their

associated probabilities. Prove that the probabilities add to one.

c$.$ Calculate the mean of the total loss distribution and show that it is equal to the mean

of the severity distribution times the mean of the frequency distribution.