[15 points] Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 8% coupon (Le., paid annually) if it is currently selling at par (i.e., $1000) and the probability distribution of its yield to maturity a year from now is as follows: State of the EconomyProbability of stateYIM 15% 896 -2% Excellent Good Poor 0.25 0.45 0.30