How is the normal distribution formula derived?

[bomba923]

How do you derive the normal distribution formula??

How was it derived?

(mu=population mean,
sigma=std. deviation)

(see below thumbnail for formula)

 

[Zurtex]

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

 

[matt grime]

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.

 

[bomba923]

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.

Good idea-i'll try just that