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Answer 1) Look up Gamma distribution in say Wikipedia or an on-line encyclopedia. This is not a simple subject.

Answer 2) The Gamma distribution is essentially a generalization of the Chi-square distribution. Multiplying a Chi-square random variable by a positive constant you get a Gamma random variable. See also the introduction to the Gamma random variable on statlect.com (see link below).

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Q: Where can I read an introduction to the Gamma distribution?
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What is the use of the Gamma distribution?

It is very frequently used in statistics. First of all, multiplying a Chi-square random variable by a constant you obtain a Gamma random variable. So, for example, most estimates of variance obtained in inferential statistics have a Gamma distribution. The Gamma distribution can also be obtained by summing exponential random variables. So, the Gamma distribution pops out in models where the exponential distribution is used (e.g. reliability, credit risk). It is also used for Internet traffic modeling. See the StatLect entry (link below) for an introduction.


What is the difference between Gamma distribution and Central limit theorem?

There is abig difference between them..gamma is a distribution but central limit theorm is just like a method or technique u use to approximate gamma to another distriution which is normal....stupid


About the history of gamma distribution?

According to the links, Karl Pearson was first to formally introduce the gamma distribution. However, the symbol gamma for the gamma function, as a part of calculus, originated far earlier, by Legrenge (1752 to 1853). The beta and gamma functions are related. Please review the related links, particularly the second one from Wikipedia.


What was the motivation for introducing the Gamma distribution?

It can be thought of as a generalization of the Chi-square distribution. See the link to a related WikiAnswer question below.


What are examples of Gamma distribution in real life?

Waiting time until failure. Modelling insurance claims.


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I apologize my question should have read what are the characteristics of a standard normal probability distribution? Thank you