"Randomness" is the key factor for the evolution of various phenomena. Directions of the evolution are determined by some specific windows of selections for random changes.

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

okay so in this video we're going to look at what are known as joint probability density functions and these are just very common uh functions that you'll encounter in again a probability or ...

The Virginia Lottery offers a game called the New Year's Millionaire Raffle for which the top prize is one million dollars. There are 375,000 tickets sold, of which 508 are winners. There are three ...

ABSTRACT: This paper derives a mathematical description of the complex stretch processor’s response to bandlimited Gaussian noise having arbitrary center frequency and bandwidth. The description of ...

In a raffle with 20 tickets, 6 tickets are drawn for prizes. The first prize winner gets $\$20$, 2 second prize winners get $\$10$, and three third prize winners get $\$5$. What is the sample space ...