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