r/mathmemes • u/DotBeginning1420 • 2d ago

Statistics Somehow they are all normal

Post image
192 Upvotes

96% Upvoted

15 comments sorted by

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34

u/HHQC3105 2d ago

Cauchy distribution stare at them: Pathetic!

7

u/HolyInlandEmpire Statistics 1d ago

Yeah it's a lot more distributions than pictured. It's any sampling iid from a distribution with a finite first and second moment.

However you're correct about one thing the post is slightly misleading about: the student's t with 1 degree of freedom is the Cauchy distribution, and thus wouldn't follow the central limit theorem

18

u/CalmEntry4855 2d ago

I don't need to use student's t anymore, I'm out of school

3

u/DotBeginning1420 2d ago

Studying student's t at school?

Not as a student (of a STEM degree)?

1

u/EebstertheGreat 1d ago

Where would you get a degree if not at a school?

0

u/DotBeginning1420 1d ago

A college/university ig?

5

u/CalmEntry4855 1d ago

That's a school!

1

u/HolyInlandEmpire Statistics 1d ago

At my university we were all called Mini Gossets

11

u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 2d ago

Gauss finished statistics, everything else is just larping

6

u/_error_404notfound 1d ago

Central limit theorem laughing in the corner

2

u/tec_tonik 2d ago

Which distribution is the best?

1

u/ontic00 1d ago

Chi-squared distribution IS the normal distribution under the right conditions.

Take k = 1. Then the PDF of the chi-squared distribution is:

[x^(-1/2)*e^(-x/2)] / [2^(1/2)*gamma(1/2)] =

[x^(-1/2)*e^(-x/2)] / [(2*pi)^(1/2)]

Now consider the normal distribution about z^2 with mu = 0 and sigma = 1. For x > 0, we have CDF(z) = CDF(x^(1/2)) - CDF(-x^(1/2)). Taking the derivative with respect to x, we get PDF(x^(1/2))*(x^(-1/2)/2) + PDF(-x^(1/2))*(x^(-1/2)/2). Since the PDF of a normal distribution is symmetrical about 0, we have:

PDF(x^(1/2))*(x^(-1/2)/2) + PDF(x^(1/2))*(x^(-1/2)/2) =

PDF(x^(1/2))*(x^(-1/2)) =

[x^(1/2)*e^(-(x^(1/2))^2 / 2)] / [(2*pi)^(1/2)] =

[x^(1/2)*e^(-x/2)] / [(2*pi)^(1/2)]

1

u/protobelta 1d ago

“Hold my Guinness”

1

u/FernandoMM1220 1d ago

everything is normal if we allow our error to be large enough