Aggregate claims S are Compound Poisson with $=2$ and severity distribution

P$($X $=1)=14,$ P$($X $=2)=34.$

For a premium of P $=6,$ an insurer covers aggregate claims and agrees to pay a dividend D equal to the excess, if any, of $75\%$ of the premium over $100\%$ of the aggregate claims. Determine the excess of premium over expected claims and dividends.

Hint: D $=$ max$\{0,4\mathrm{.}5$ S$\}.$