Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and ...

Abstract: The approximation of a nonlinear function of a random variable by a linear function is considered. An exponential function, which arises in problems such as random sampling and random ...

Abstract: It is well known that the entropy H(X) of a discrete random variable X is always greater than or equal to the entropy H(f(X)) of a function f of X, with equality if and only if f is ...

The FIND function allows you to find a text string within another. It returns the position at which a character or string begins within another text string. The LEN function calculates the length of ...

The Random123 library is a collection of counter-based random number generators ( "CBRNGs") for CPUs (C and C++) and GPUs (CUDA and OpenCL), as described in Parallel Random Numbers: As Easy as 1, 2, 3 ...

Python has a behavior that is not universal among programming languages, and if you have experience with, say Java, you might find this surprising. Let’s walk through what’s happening. Why does this ...

Forecasting for any small business involves guesswork. You know your business and its past performance, but you may not be comfortable predicting the future. Using Excel is a great way to perform what ...

Many types of economic problems require that we consider two variables at the same time. A typical example is the relation between price of a commodity and the demand or supply of that commodity. The ...