# Finding the central rate of mortality under a piecewise UDD assumption.

Suppose that, in a certain group of lives, half of the deaths between ages $$x$$ and $$x + 1$$ are distributed evenly over the first 4 months of that year, i.e. between ages $$x$$ and $$x+ \frac{1}{3}$$, and the remainder are distributed evenly over the rest of the year. Find $$m_{x}$$, the central rate of mortality, in terms of $$q_{x}$$.