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**White_Owl****Member**- Registered: 2010-03-03
- Posts: 99

I do not understand it.

Well, I kinda understand its meaning, but I am not sure how to read it or calculate it on a real numbers.

For example, if we have a

Now, how to calculate it for lets say k=10? or for k=100?

What goes for X in the inequality and what is the result of Pr() function?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

That inequality means that the probability of the difference between X and mu being greater or equal to k*sigma is less than or equal to 1/k^2.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**White_Owl****Member**- Registered: 2010-03-03
- Posts: 99

Yes, I read the definition, but it is not enough, I need a practical example.

Definition also says that it is true for all k>0.

So, if we have k=10:

Which X should I put here to see the truth of this inequality?

*Last edited by White_Owl (2013-02-19 11:31:37)*

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

You need to find the probability that |X-3.2|>=18.3 . You can do that by summind the probabilities of all values of X for which that is hreater than 18.3 (which is in this case 0). And you probably know that 0<=0.01 .

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**White_Owl****Member**- Registered: 2010-03-03
- Posts: 99

Ok, then lets take the k=2.

In that case we have two X which satisfy the inequality in parenthesis: 7 and 8.

Now what is the values of

Can you tell me the values for

What is the value of Pr(TRUE)???

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,606

They are both 1. But if you multiply 1 by the probability that X is in fact 7 (or 8), and then sum over all values of X, you will get the probability.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**White_Owl****Member**- Registered: 2010-03-03
- Posts: 99

I am sorry, I do not understand your answer.

You said a=b=1? Where did 1 come from?

What exactly should I sum and why?

I am now even more confused...

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**White_Owl****Member**- Registered: 2010-03-03
- Posts: 99

Well? Does anyone have an answer?

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**Avon****Member**- Registered: 2007-06-28
- Posts: 80

White_Owl,

Suppose you wanted to find

Hopefully it is obvious that

so

Similarly, you have observed that

so

What anonimnystefy is referring to in post #6 is that

where if is true and 0 if it is false.

This is also equal to

I hope this helps.

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**White_Owl****Member**- Registered: 2010-03-03
- Posts: 99

Oh! So inequality inside parenthesis in the probability arithmetic means sum of probabilities of all events which satisfy the inequality?

Well, it is kinda strange and unintuitive, but ok. I guess there is some logic in that and I would have to live with it...

But why not just write something like:

I think this would be more clear. Don't you think?

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