What is the relationship between a random variable N(0,1) and other continuous random variables?

What is the relati开发者_运维问答onship between a random variable with normal distribution (N(0,1)) and other continuous random variables?

Can you give me an example?

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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