Central Limit Theorem conceptual understanding and memory

In nature and production, some of the phenomena influenced by many independent random factors, if the impact of each factor generated are tiny, the overall effect can be seen as the normal distribution.

Take n random variables, assuming that eventually comply with the above conclusion - thought to meet the normal distribution, the normal distribution with ideas to be translated into the standard normal distribution:

Take the n random variables, and of these n samples of random variables (assuming each random variable takes a sample),

Prerequisites: Normally (((normally distributed random variable) minus (which is expected value)) / standard deviation) is the standard normal variable obtained;

 

Now we assume that we have taken to the (n random variables) a normal distribution and variance and expected value of each random variable are the same (n independent and identically distributed random variables, and does not have to be a normal distribution);

Then ((n sample values ​​and random variable) minus (n times the random variable expected value)) / (n random variables standard difference)) is obtained in compliance with the final standard normal random variable;

 

The above are just already know from the case of the conclusion of the thrust reverser formula, because the final conclusion is really a normal distribution (poor root n times the standard random variable) than the process to remember more, on standard deviation n random variables is explained as follows: (n is added to a variance of a random variable) and then the entire square root, because brackets made after a n, then there must be a square root n-root;

Focusing on understanding, but also cover the case.