Monash University

Continuous random variables

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

One Random Variable: Fundamentals

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 ...
JSTOR Daily

Conditional Expectations of Random Variables Without Expectations

Let (Ω, F, P) be a probability space, and let X be a random variable defined on (Ω, F, P). If A is a sub σ-field of F, then E(X ∣ A) is the a.s. unique A measurable function such that, for all A ε A, ...
IEEE

Novel Methods to Construct Empirical CDF for Continuous Random Variables using Censor Data

Abstract: We deal with the problem of creating empirical CDF (ECDF) for a continuous random variable X, defined as time of an event of interest, such as failure or repair. The data sample to construct ...
JSTOR Daily

Convergence of series and almost sure convergence for weighted random variables under sub-linear expectations

In this paper, convergence of series and almost sure convergence are established for weighted random variables under a sub-linear expectation space. Our results are very extensive versions which ...