On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. Suppose the probability density function for the length of time it takes a ...

Overview: In probability and statistics, it is important to understand the mean and variance for any random variables. In many applications, it is straightforward to simulate the random variable Y ’s, ...

The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given as x 0 1 2 3 4 p(x ...

This paper is concerned with the determination of tight lower and upper bounds on the expectation of a convex function of a random variable. The classic bounds are those of Jensen and ...

Addresses the topics of probability, random variables, discrete and continuous densities, expectation and variance, special distributions (binomial, Poisson, normal, etc.), moment generating functions ...

Abstract: Monte Carlo simulation has been widely used as a standard tool for estimating expectations. In this paper we develop a variance reduction technique for a particular case when the expectation ...