The problem statement says “arbitrary real numbers”, so the domain of your function P is -infinity to +infinity. P represents a probability distribution, so the area under the curve is equal to 1. P is strictly increasing, so… I’m having trouble visualizing a function that meets all these conditions.
You say “any” such function… perhaps you could give just one example.
In this case P is the cumulative distribution function, so it has to approach 1 at infinity, rather than the area under the curve being 1. An example would be 1/(1+exp(-x)).
The problem statement says “arbitrary real numbers”, so the domain of your function P is -infinity to +infinity. P represents a probability distribution, so the area under the curve is equal to 1. P is strictly increasing, so… I’m having trouble visualizing a function that meets all these conditions.
You say “any” such function… perhaps you could give just one example.
In this case P is the cumulative distribution function, so it has to approach 1 at infinity, rather than the area under the curve being 1. An example would be 1/(1+exp(-x)).
Actually, for any given P which works, P’(x)=P(x)/10 is also a valid algorithm.