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Random numbers (or deviates) can be generated for many distributions, including the Normal distribution. Programs like Excel include a function which will generate normal random variables. In Excel, you enter +norminv(+rand(),mean,stand dev). The formula can be copied down to generate many deviates. Hitting F9 will produce a new series. Be sure to enter a positive number for the standard deviation. Theory: Let X be a uniformly distributed random variable from 0 to 1. We want to generate deviates of distribution with a pdf of f(x) and a cumulative distribution of F(x) with F-1(x), the inverse CDF known. Generate a uniform deviate, a, and then calculate b = F-1(a) which will be distributed according to f(x). The related links are unfortunately quite mathematical. The problem with the normal distibution is that the inverse cumulative is not a simple equation, so table lookup is usually the fastest solution.
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Which distribution do not have mean?
The Cauchy or Cauchy-Lorentz distribution. The ratio of two Normal random variables has a C-L distribution.
What is importance of central limit theorem?
The importance is that the sum of a large number of independent random variables is always approximately normally distributed as long as each random variable has the same distribution and that distribution has a finite mean and variance. The point is that it DOES NOT matter what the particular distribution is. So whatever distribution you start with, you always end up with normal.
Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
Why you prefer normal distribution as compare to others in statistics?
Perhaps a mistaken impression, after completing an initial course in statistics, is that one distribution is better than another. Many other distributions exists. Usually, introductory statistics classes concern confidence limits, hypothesis testing and sample size determination which all involve a sampling distribution of a particular statistic such as the mean. The normal distribution is often the appropriate distribution in these areas. The normal distribution is appropriate when the random variable in question is the result of many small independent random variables that have been are summed . The attached link shows this very well. Theoretically, a random variable approaches the normal distribution as the sample size tends towards infinity. (Central limit theory) As a practical matter, it is very important that the contributing variables be small and independent.
The usual sampling distributionof the difference between means is a what?
There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.There is no such thing as "the usual sampling distribution". Different distributions of the original random variables will give different distributions for the difference between their means.
