Suppose we have a continuous distribution f over a finite support [a,b] and know that for some finite set of values between a and b {v1, v2, ... vn} the CDF[f,v1]=q1, CDF[f,v2]==q2, ...CDF[f,vn]=qn. Essentially, we know the CDF of the distribution at various points on the interior of the distribution, but we don't know it over the entire domain [a,b]. How do we figure out the distribution f with maximal entropy that satisfies the constraints?