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: 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 ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

Continuous Variable: can take on any value between two specified values. Obtained by measuring. Discrete Variable: not continuous variable (cannot take on any value between two specified values).

Bernstein polynomial estimation provides a robust nonparametric technique for approximating both density and distribution functions. Based on the properties of Bernstein polynomials, which uniformly ...