$9\mathrm{.}13(*)$ For a certain group, aggregate claims are uniformly distributed over $(0,10).$ Insurer

A proposes stop$-$loss coverage with a deductible of $6$ for a premium equal to the expected

stop$-$loss claims. Insurer B proposes group coverage with a premium of $7$ and a dividend

$($a premium refund$)$ equal to the excess, if any, of $7k$ over claims. Calculate $k$ such that the

expected cost to the group is equal under both proposals.