And they say "the internet is dead" Here is some entertainment.
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Here's the thing about that formula for the gaussian distribution. It looks scary, right? Look at all those symbols! The first thing is to realize you are just looking at:
y=e^x but changed in a few ways.
Don't worry about the fraction at the front. (1/sqrt(2pi sigma^2)) That is just a constant.
Now y=e^x is the exponential. It increases faster the larger it is. It shoots up to the right and goes to zero to the left.
1/Consider also y=e^{x*x} that one looks like an over enthusiastic parabola.
So, when you take y=e^-{x*x} you get a nice hump, it looks almost like the normal curve already.
In fact, everything else is just about moving it around and making the mean and SD do what you'd expect.
Not bad at all. 2/2
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Consider also y=e^{x*x} that one looks like an over enthusiastic parabola.
So, when you take y=e^-{x*x} you get a nice hump, it looks almost like the normal curve already.
In fact, everything else is just about moving it around and making the mean and SD do what you'd expect.
Not bad at all. 2/2
I love the gaussian distribution so much but my students get so upset when they see the formula it makes me sad.
It's REALLY not that bad I promise. The stats people just want it to have an area under the curve equal to one. So they decorate it with all of this... stuff... It's useful.
But the essence of what it is? It's just e raised to the negative x squared. Noting to be upset about.
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I love the gaussian distribution so much but my students get so upset when they see the formula it makes me sad.
It's REALLY not that bad I promise. The stats people just want it to have an area under the curve equal to one. So they decorate it with all of this... stuff... It's useful.
But the essence of what it is? It's just e raised to the negative x squared. Noting to be upset about.
@futurebird the fact that integrating that bad boy is a pain in the ass does not help either.
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@futurebird the fact that integrating that bad boy is a pain in the ass does not help either.
The "fancy coffee table" (1/sqrt(2pi sigma^2)) helps things a little...
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I love the gaussian distribution so much but my students get so upset when they see the formula it makes me sad.
It's REALLY not that bad I promise. The stats people just want it to have an area under the curve equal to one. So they decorate it with all of this... stuff... It's useful.
But the essence of what it is? It's just e raised to the negative x squared. Noting to be upset about.
@futurebird hey I have been texting you trying to figure out whether we're meeting tomorrow or not
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The "fancy coffee table" (1/sqrt(2pi sigma^2)) helps things a little...
@futurebird @javier The context that finally clicked for me was:
1. maximize entropy for pdf with no constraints -> uniform distribution;
2. maximize entropy for pdf with fixed mean -> exponential;
3. maximize entropy for pdf with fixed mean + finite variance -> gaussian. -
@futurebird @javier The context that finally clicked for me was:
1. maximize entropy for pdf with no constraints -> uniform distribution;
2. maximize entropy for pdf with fixed mean -> exponential;
3. maximize entropy for pdf with fixed mean + finite variance -> gaussian. -
@futurebird the fact that integrating that bad boy is a pain in the ass does not help either.
To learn how to do it "naturally" you'd need to learn an awful lot of integration tips and tricks.
I think of it as something that exists in the way that it is *because* it has to integrate to 1. So if you derive it so it's a distribution, you have kind of already integrated it.
(don't know if I explained that well. I'm just saying don't feel bad if it stumps you. It's artificial. )
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I love the gaussian distribution so much but my students get so upset when they see the formula it makes me sad.
It's REALLY not that bad I promise. The stats people just want it to have an area under the curve equal to one. So they decorate it with all of this... stuff... It's useful.
But the essence of what it is? It's just e raised to the negative x squared. Noting to be upset about.
@futurebird Statisticians are only good at two mathematical operations: adding zero and multiplying by 1.
So we just squint at formulae and say "it looks kind of normal with a constant of proportionality" and move on.
For fun, we ask normal people to calculate the mean of a Cauchy distribution. -
@futurebird Statisticians are only good at two mathematical operations: adding zero and multiplying by 1.
So we just squint at formulae and say "it looks kind of normal with a constant of proportionality" and move on.
For fun, we ask normal people to calculate the mean of a Cauchy distribution.That's mean.
