Continuous Function Averages
Standard Average
The average value of \(f(x)\) from a to b is:
\[{\int_{a}^{b} f(x) dx \over b - a }\]
Weighted Average
The average value of \(f(x)\) from a to b with weights of \(w(x)\) is:
\[{ \int_{a}^{b} w(x)*f(x) dx \over \int_{a}^{b} w(x) dx }\]
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Proof of Work Hashrate Equilibrium Maths
Note: this is simply a thought experiment without any real practical use cases. It depends on knowing the cost function...