I am trying to define an AI domain in which I need to define the probability $p_i,$ of a variable $v_i$ having a value 1 or 0. $p_i$ may range anywhere from 0 to 100%. In my problem i goes from 1 to 83. $p_i$ has the following restriction:
I want on average for 47 of the variables $v_i$ to take value 1, so
And they need to have an extra characteristic due to my domain which is obeying this formula:
Any thoughts on how do I solve this?
(For reference, here is the original link.)
EDIT (from comments):
I am trying to define an AI domain, those are probabilities (p_i) of several variables being 1 or 0. But I have to have more 1's on smaller i's and more 0's on larger ones. On average, I should have 47 1's, meaning that the sum of their probability should be 47.
I will actually be varying the values of the 80% and the 47, but I thought it would be easier to post it like that.