What is the relationship between a R.V N(0,1) and others continuous random variables

Question

Hello.

I have a question. I need to kwon what is the relationship between a Random Variable with Normal distribuation (N(0,1)) and others continuous random variables.

Can you write to me an example?

Thank You

Hola a todos.

Necesito saber qué relación existe entre una variable aleatoria Normal (0,1) y cualquier variable aleatoria continua. Además, me vendría bien un ejemplo.

Gracias por vuestra ayuda

Answer 1

This chart will answer your question. The arrows indicate relationships between probability distributions. Click on an arrow to see details of the relationship.

Answer 2

I found the answer to my question.

Levy and Lindeberg formulated the levy-Lindeberg centra limit theorem:

For {wt} an iid sequence, Ewt=mu, and var(wt)=s2:

Let W=the average of the T wt's. Then: T1/2(W-mu)/s converges in distribution as T goes to infinity to a N(0,1) distribution