Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 8% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows: see attachment, can you please show the equation used to determine price of the coupon bond

3- Derive the probability distribution of the 1-year I-[PR on a 30-year US. Treasury bond with an 3% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows: State of the Economy Probability YTM Boom 0.26 i 1.0% Normal growth 0.59 8.0 RecesEiOn 0.30 10 For simplicity. assume the entire 8% coupon is paid at the end of the year rather than every 6 months