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 ...

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 ...

Abstract: The characteristic function of fuzzy random variables is defined based on the average chance distribution function. Then, the mathematical properties of the characteristic function, which ...

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

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 ...

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 ...

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 ...

Economists are interested in examining types of relationships. For example an economist may look at the amount of money a person earns and the amount that person chooses to spend. This is a ...