Overview: In probability and statistics, it is important to understand the mean and variance for any random variables. In many applications, it is straightforward to simulate the random variable Y ’s, ...

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

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, ...

On a certain track team, the runners all take between 4 and 7 minutes to finish a mile. Suppose the probability density function for the length of time it takes a ...

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 ...

1 Pan African University, Institute for Basic Sciences, Technology and Innovation (PAUISTI), Nairobi, Kenya. 2 Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture ...

We have applied the Lie-Trotter operator splitting method to model the dynamics of both the sum and difference of two correlated constant elasticity of variance (CEV) stochastic variables. Within the ...

$\def \bb#1{{ \mathbb{#1} }}$ $\def \P#1{{ \mathbb{P} \left(#1\right) }}$ $\def \E#1{{ \mathbb{E} \left(#1\right) }}$ $\def \Var#1{{ \text{Var} \left(#1\right ...