Abstract: Fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables. The variance is a fundamental concept for fuzzy random variables. Due to the ...

In this paper we define the concept of a normal fuzzy random variable and we prove the following representation theorem: Every normal fuzzy random variable equals the sum of its expected value and a ...

Abstract: In this chapter, the authors discuss sample spaces, basic probability theory and random variables. Conditional probability leads to tree diagrams and the Bayes formula. Bernoulli trials pave ...

The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...

Suppose a1, a2,... is a sequence of real numbers with an → ∞. If $\lim \sup(X_1 + \cdots + X_n)/a_n = \alpha$ a.s. for every sequence of independent nonnegative uniformly bounded random variables X1, ...

A continuous random variable is a type of variable that can take on any value within a given range. Unlike discrete random variables, which have a countable number of outcomes, continuous random ...

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...