Normal functions of normal random variables

Distributions of Functions of Normal Random Variables

The unit or standard normal random variable U is a normally distributed variable with mean zero and variance one, i. e. U ∼ N(0, 1). Note that if x ∼ N(µ, σ 2) that x − µ σ ∼ U ∼ N(0, 1) (1) Thus to simulate a normal random variable with mean µ and variance σ 2 , we can simply transform unit normals, as x ∼ µ + σU ∼ N(µ, σ 2) (2) Consider n independent random variables x i ∼ N(µ, σ 2), then x ∼...

Distributions of Functions of Normal Random Variables

Formalization of Normal Random Variables in HOL

Many components of engineering systems exhibit random and uncertain behaviors that are normally distributed. In order to conduct the analysis of such systems within the trusted kernel of a higherorder-logic theorem prover, in this paper, we provide a higher-order-logic formalization of Lebesgue measure and Normal random variables along with the proof of their classical properties. To illustrate...

Comparison of Different Techniques to Generate Normal Random Variables∗

This exercise aims at exploring different techniques for creating a random variable X according to a normal distribution with zero mean and unit variance. The methods include the use of an inverse cumulative distribution function, the Box–Muller method, the polar technique and the application of the Central Limit Theorems to uniform random variables. The normal random variables generated by the...

I the Distributions of Quadratic Forms on Normal Random Variables