John wants to purchase a bond which will pay him X thousand

John wants to purchase a bond which will pay him X thousand dollars after two years, where X is equally likely to be any of the numbers in the set {0,1,2,3,4,5}. John believes that the continuously compounded rate of interest, R, is independent of X and has a uniform distribution on the interval (0.04, 0.08). The present value of this bond after two years is given by V = Xe^(-2R). Compute the mean of the present value of the bond.

Solution