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 ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Colorblindness is caused by a recessive gene on the X chromosome. Since men have only one X chromosome, if a man carries the colorblindness allele (gene form), he will have the trait. Women have two X ...

Abstract: The Beckmann distribution has a wide range of applications in radio-frequency communications, free-space optical (FSO) communications, and underwater wireless optical communications (UWOC).

A continuous-time process is called white noise if for arbitrary n, sampling at arbitrary time instants t_1, t_2, ..., t_n, the resulting random variables, X_{t_1}, X ...

A random variable is a mathematical function that maps outcomes of random experiments to numbers. It can be thought of as the numeric result of operating a non-deterministic mechanism or performing a ...