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 ...

Random-number functions and CALL routines generate streams of random numbers from an initial starting point, called a seed, that either the user or the computer clock supplies. A seed must be a ...

1: The time required for servicing transmissions is normally distributed with = 45 minutes and = 8 minutes. The service manager plans to have work begin on the transmission of a customer’s car 10 ...

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. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Abstract: Given the joint probability density function (pdf), pX(xl, ..., xN), of the random variables x1, xN, a new method is developed for determining the pdf of the ratio f(X)lg(X) where f and g ...

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 ...

We consider functions φ having the following properties: φ(0)=1, φ(-t) = φ(t) φ is continuable to a function analytic in the upper halfplane. We discuss the problem under which conditions such a ...

The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...

Amusement park patrons, wanting to go on a log ride, might not have to wait in line at all, they might have to wait for hours, or the wait could be anywhere in between. For a random log rider, the ...