Derlve the probability distribution of the $1-$year HPR on a $30-$year U$.$S$.$ Treasury bond with a $3\mathrm{.}5\%$ coupon If It is

currently selling at par and the probability distribution of Its yleld to maturity a year from now is as shown in the table

below. $($Assume the entire $3\mathrm{.}5\%$ coupon is pald at the end of the year rather than every $6$ months. Assume a par value

of $$100.)$

Note: Leave no cells blank $-$ be certaln to enter $"0"$ wherever required. Negatlve values should be Indlcated by a

minus sign. Do not round Intermedlate calculatlons. Round your answers to $2$ decimal places.