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, ...

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 ...

The random variable 2−3X is of the form aX+b, with a=−3 and b=2. Thus, Var(2−3X)=(−3)2Var(X)=9⋅2=18. Is it always true that $E[X^2]≥(E[X])^2$? We know ...

This paper investigates how the major outcome of a confirmatory factor investigation is preserved when scaling the variance of a latent variable by the various scaling methods. A constancy framework, ...

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 ...