Abstract: In this correspondence, we give a sufficient condition for the exponential decay of the tail probability of a nonnegative random variable. We consider the Laplace-Stieltjes transform of the ...
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, ...
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 ...
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 ...
Example 1: A coin is flipped. Random variable X takes the value 1 if the coin lands heads, and X takes the value 0 if the coin shows tails. Example 2: Three balls are drawn without replacement from a ...
This note suggests that expressing a distribution function as a mixture of suitably chosen distribution functions leads to improved methods for generating random variables in a computer. The idea is ...
ABSTRACT: The purpose of this article is to develop a new methodology to evaluate the statistical characteristic of the response of structures subjecting to random excitation, by combining the Finite ...