(a) The bilateral exponential is defined by $${ \frac{1}{2}\alpha e^{-\alpha|x|} }$$. Here, $${ \alpha }$$ is the scale parameter. This distribution has an expected value of $${ 0 }$$ and a variance ...

Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, “Probability is the most important concept in modern science, especially as nobody has the ...

remove-circle Internet Archive's in-browser bookreader "theater" requires JavaScript to be enabled. It appears your browser does not have it turned on. Please see ...

Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...

A Matlab toolbox for solving the generalized density evolution equation (GDEE) in the probability density evolution method (PDEM) by finite difference method.

Abstract: Probability density function (PDF) curves are among the few charts on a Cartesian coordinate system that are commonly presented without y-axes. This design decision may be due to the lack of ...

The mathematician Daniel Litt has driven social media users to distraction with a series of simple-seeming but counterintuitive probability puzzles. In late January, Daniel Litt posed an innocent ...

Abstract: Non-linear filters consider probability density functions in various non-parametric representations. They often suffer from the curse of dimensionality. Computation of weights over a grid of ...