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 ...

A **variable** is said to be **random** if its values are determined by a random experiment. In other word, **random variable** is a numerical description of the ...

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 ...

In this paper, we provide Poincaré-type upper and lower variance bounds for a function g(X) of a discrete integer-valued random variable (r.v.) X, in terms of the (forward) differences of g up to some ...

Continuous Variable: can take on any value between two specified values. Obtained by measuring. Covariance: a measure of the direction of the linear relationship between two variables. Discrete ...