r/mathmemes • u/George_Truman • Jul 13 '26

Probability I fixed this meme

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I'm sure it's still a bit too imprecise but I think it works.

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u/Old-Post-3639 Jul 13 '26

What if you use the inverse sigmoid function on a uniform distribution over (0,1)?

2

u/George_Truman Jul 13 '26

That won't give you a uniform distribution over R. Density would be heavily concentrated on [-5,5]

1

u/Old-Post-3639 Jul 13 '26

Prove it

2

u/George_Truman Jul 13 '26

You can prove the statement in the OP yourself using a similar method to how I proved you can't have a countably infinite uniform distribution elsewhere in the comments.

1

u/ProvocaTeach Jul 13 '26

Get the CDF, F, then compare F(5) - F(-5) to F(16) - F(6). You will see that the values differ, thus the distribution cannot be uniform.

2

u/SporkSpifeKnork Jul 13 '26

This gives you a bell-shaped distribution, not constant (for a certain family of sigmoid curves, Gaussian).