Convexity

If exists, use the definition $2\mathrm{.}11$ and

to show that for a convex function $($ for a concave function Formula$2\mathrm{.}11).$

For a bond with periodic coupon payments, the th cash flow is discounted using $.$ Show that is a convex function of $.$

Show that Formula $2\mathrm{.}5,$ for the price of a coupon bond is a convex function of yield. $[$Hint: Use the result from part $($b$)$ of this problem.$]$