Figure 1: Snapshots of the quantum Wigner distribution and of the classical probability density in phase space of an evolving chaotic system.

We prove that for a diffusion process the first-passage-time p.d.f. through a continuous-time function with bounded derivative satisfies a Volterra integral equation of the second kind whose kernel ...

Probability Notes: Check detailed notes on Probability, designed to help class 10 and class 12 students deepen their understanding of the topic and enhance their exam preparation.

Let's say I roll two dice, a d8 and a d12… How do I calculate the probability that the d12 will a) win, b) be equal, c) lose? There is probably a name for this equation, but my google-fu is lacking.

A simple and efficient numerical procedure for the solution of the integral equation is provided and its convergence is briefly discussed. Use of this equation is finally made to obtain closed-form ...

What Is the Normal Distribution? The normal distribution formula is based on two simple parameters— mean and standard deviation —that quantify the characteristics of a given dataset.

That conclusion is based on research using the Drake equation: a formula with seven variables that explores the chance detectable extraterrestrial civilizations exist.