$1.$ An insurer with net worth $100$ has accepted $($and collected the premium for$)$ a risk X with the following probability distribution: Pr$($X $=0)=$ Pr$($X $=51)=1/2$ : What is the maximum amount G it should pay another insurer to accept $100\%$ of this loss? Assume the first insurer's utility function of wealth is u$($w$)=$ log w$.2.$ An insurer, with wealth $650$ and the same utility function u$($w$)=$ log w$,$ is considering accepting the above risk. What is the minimum amount H this insurer would accept as premium to cover $100\%$ of the loss?