Mathematical Formulation

NOTE: If you don't post some proposal and convince me that you have the needed experience and knowledge, your bid will be ignored. Given a variable “p” and a function “r” such that x>=r(p)<=y and an integer or r(p)=”Unknown”; x<0 (negative integer) and y>0 (positive integer). That is, function “r” either returns an integer between “x” and “y” or “Unknown”. Function “r” runs at random time intervals and the history of all values of r(p) are stored in list h(p)={(p0, t0), (p1, t1), (p2, t2),…(pn, tn)}, such that (pi, ti) is the value of r(p) at time i, and t0<t1<t2<…pn. Each time r(p) runs, the result is added to h(p) if it is known (integer). If r(p)=Unknown, then the value of the r(p) starts increasing or decreasing gradually with time but also based on the values stored in h(p) until it becomes 0 (obviously that will happen only if r(p) always returns “Unknown” every time it is executed). That is, based on the curve represented by h(p). I want a formal mathematical definition of the problem and a function that can compute/predict the integer value of r(p) when r(p)=”Unknown” based on (1) The length of h(p); and (2) The values stored at h(p). In other words, if we represent h(p) as a curve on the plane, and r(p)=”Unknown”, then what is the expected value of r(p) if the curve is getting closer to “0” every time r(p) is unknown? Considerations: If the list h(p) is long (has many values) and the values are very close to “x” and/or “y”, then it will take longer to be 0. On the other hand, if h(p) has values that are close to “0” then it will take shorter to become “0”. That is, the curve should always look somewhat normal. Please describe your approach and how you will solve this problem. Also, let me know if you have any questions. I will provide you with more details as we communicate and exchange messages.