- #1
How is the normal distribution formula derived?
- Context: Undergrad
- Thread starter bomba923
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Discussion Overview
The discussion revolves around the derivation of the normal distribution formula, exploring its mathematical foundations and connections to other statistical concepts. Participants consider both theoretical and practical aspects, including the relationship between binomial distributions and the normal distribution.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
Main Points Raised
- One participant inquires about the derivation of the normal distribution formula, specifically referencing the population mean (mu) and standard deviation (sigma).
- Another participant suggests that the proof of the normal distribution is relatively simple when applying the definition of standard deviation, although they do not recall the details.
- A participant proposes examining histograms of binomial distributions for a large number of trials, noting that these histograms approximate the normal distribution and that the error in using the normal distribution decreases as the number of trials increases.
- It is mentioned that any function from R to R whose integral over R equals 1 defines a probability distribution, indicating that normal distributions are prevalent in real-life phenomena.
- The Central Limit Theorem is referenced as a powerful concept that underpins the relationship between binomial and normal distributions.
Areas of Agreement / Disagreement
Participants express various viewpoints on the derivation and understanding of the normal distribution, with no consensus reached on a singular method of derivation or explanation.
Contextual Notes
The discussion includes assumptions about the familiarity with statistical concepts such as standard deviation and the Central Limit Theorem, which may not be universally understood. The relationship between binomial and normal distributions is suggested but not fully explored.
- #2
Zurtex
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Have you attempted it?
I don't remember it off by heart but I do remember the proof on the board being quite simple once you apply the definition of S.D
I don't remember it off by heart but I do remember the proof on the board being quite simple once you apply the definition of S.D
- #3
matt grime
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To view the question slightly differently, have you plotted histograms of binomial distributions for a large number of trials? It approximates the normal distribution, ie the graphs agree, and it can be shown that as n goes to infinity that the exponential formula is "correct" (ie the error in using it goes to zero.
Note that ANY function from R to R whose integral over R is 1 defines a probability distribution, it is up to us to find real life situations for when to use them. It so happens that normal distributions appear to describe many real life phenomena.
Look up the Central Limit Theorem to see why it's so powerful.
Note that ANY function from R to R whose integral over R is 1 defines a probability distribution, it is up to us to find real life situations for when to use them. It so happens that normal distributions appear to describe many real life phenomena.
Look up the Central Limit Theorem to see why it's so powerful.
- #4
bomba923
- 759
- 0
matt grime said:
Good idea-i'll try just that
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