Suppose an insurance buyer has initial wealth Wo, uses as utility function u(w)=-e^(-w) and faces a risk X. The distribu

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Suppose an insurance buyer has initial wealth Wo, uses as
utility function u(w)=-e^(-w) and faces a risk X. The distribution
of X is determined by some probability density function f(x). The
insurance buyer wants to determine the maximal premium ρ he/she is
willing to pay to get rid of the risk X based on the expected
utility. Calculate ρ if X~exp(2), i.e. f(x)=2e^(-2x) for x>=0.
How can the minimum premium an insurer will ask for insurance be
calculated? Under what condition an insurance contract is
possible?
I have the solution but I do not understand it. Please as
detailed as possible explained