Discrete Distributions (Alatissa, Probability Theory Expert)

Shpilevoy wrote:

Alatissa wrote: Relative deviation
100/500=0.2
You can make a simulation in Excel and compare.
And no matter how many times I update the thousand generated =RANDBETWEEN(0;1)
I haven't seen this figure even higher than 0.1.
Therefore, it is not advisable to make more throws.

It turns out that there is a calculated threshold (norm), and when a fact violates it, something abnormal is happening.
I think for our purposes it is enough to set a boundary
μ−2σ
There's no point in delaying the drop until the third sigma.

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Mathematical expectation (μ ) is the average value of a random variable. Mu.

Standard or root-mean-square deviation (σ ) is the most common indicator of the dispersion of values of a quantity relative to the mathematical expectation. Sigma.

The three sigma rule is that in a normal distribution, almost all values of a quantity with a probability of 0.9973 lie no further than three sigmas in either direction from the mathematical expectation, that is, they are in the range [μ−3σ;μ+3σ].

Approximately 99.7% of all values are within three sigma of the expected value, about 95% are within two sigma, and about 68% of values are within just one sigma.
Values that fall outside the 3 sigma range are considered gross errors. A large number of such errors may indicate that the distribution is not actually normal. This is the practical benefit of the 3 sigma rule.
I'll comment on this post for now. I'll gradually follow up with others.
Shpilevoy describes the normal distribution law.

Normal distribution law for continuous random variables.


But discrete random variables are a little different.
These are the variables whose values are countable. They are always integer values.


* Number of hits on the target with n shots. Accepted values are 0…n
* The number of heads in n coin tosses. Accepted values are 0…n
* The number of points rolled when throwing a dice. The random variable takes one of the values {1,2,3,4,5,6...}

Alatissa wrote:

Shpilevoy wrote:
We look, as before, no deeper than 113 spins (for the 2/3 law)...

There is no such law

Alatissa wrote:

Shpilevoy wrote:
We look, as before, no deeper than 113 spins (for the 2/3 law)...

There is no such law

Proof of the Law of "Two-Thirds"
Given: 37 different numbers on a roulette wheel.
Prove it: in 37 spins, 2/3 of the 37 numbers come up.