Derivation of normal distribution

In summary, the conversation discusses the request for a coherent derivation of the normal distribution for someone with a basic understanding of calculus and statistics. The person asking for help has already looked at top Google results and is looking for personal recommendations or sources that provide a clearer understanding of the derivation. The possibility of using either the limit of the binomial distribution or the central limit theorem as a starting point is also mentioned.
  • #1
wil3
179
1
Hello! Would someone or several people mind posting a link to a coherent derivation of the normal distribution? Assume that the person reading it is a total moron with a multivariate calculus and AP Statistics background.

I've already looked at the top google results, so save yourself the trouble of copypasta'ing. I'm looking for any sources that you personally thought really helped you understand the derivation of it, or that in general helped show its origins.

Thank you very much.
 
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  • #2
When you ask for a derivation, you need to specify a starting point.

Possibilities:
1) Limit of binomial distribution as number of trials becomes infinite.
2) Central limit theorem.
 
  • #3
Central Limit Theorum seems cooler. Thanks for pointing that out!
 

What is the normal distribution?

The normal distribution is a statistical concept that describes the distribution of a set of values as a symmetrical bell-shaped curve. It is also known as the Gaussian distribution or the bell curve.

What is the purpose of deriving the normal distribution?

The purpose of deriving the normal distribution is to mathematically model and understand the behavior of a large number of random phenomena. It is a widely used tool in statistics and probability, and many natural and social phenomena can be approximated by a normal distribution.

How is the normal distribution derived?

The normal distribution is derived using calculus and the central limit theorem. The central limit theorem states that when a large enough number of independent random variables are added together, the resulting distribution will be approximately normal. This allows for the derivation of the normal distribution from simpler distributions, such as the binomial or exponential distributions.

What are the properties of the normal distribution?

The normal distribution is characterized by its mean, which is the center of the curve, and its standard deviation, which measures the spread of the data around the mean. It is a continuous distribution, meaning that the probability of any specific value is infinitesimally small. It is also symmetric around the mean, with 50% of the data falling on either side of the mean.

What are the applications of the normal distribution?

The normal distribution has numerous applications in various fields, including finance, biology, psychology, and engineering. It is commonly used in hypothesis testing, confidence intervals, and regression analysis. It is also used in quality control and process control to monitor and improve processes. Additionally, many standard statistical tests and models assume a normal distribution for the data.

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