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 ...

The PMF function that we saw before works great for inspecting discrete random variables and calculating their expected values. However, we did see that when moving towards continuous random variables ...

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).

The PMF function that we saw before works great for inspecting discrete random variables and calculating their expected values. However, we did see that when moving towards continuous random variables ...

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 ...

The COS method was introduced in Fang & Oosterlee (2008) and then was applied to pricing a variety of stock options for continuous random variables. This paper adapts the Fourier-cosine series (COS) ...

In the board game "Chick-a-Pig," a cow that sits in the center of the board and creates an obstacle for players attempting to move across the board. On each turen, a player rolls a die to determine ...

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, ...