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You are not logged in. #1 20130220 09:43:20
Chebyshev's InequalityI do not understand it. For example, if we have a pmf table: 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? #2 20130220 09:45:48
Re: Chebyshev's InequalityThat 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. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #3 20130220 10:31:02
Re: Chebyshev's InequalityYes, I read the definition, but it is not enough, I need a practical example. Which X should I put here to see the truth of this inequality? Last edited by White_Owl (20130220 10:31:37) #4 20130220 10:46:10
Re: Chebyshev's InequalityYou need to find the probability that X3.2>=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 . The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20130220 11:33:23
Re: Chebyshev's InequalityThey 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. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #9 20130222 14:47:54
Re: Chebyshev's InequalityWhite_Owl, Hopefully it is obvious that exactly when or or , so Similarly, you have observed that exactly when or , 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. #10 20130223 16:14:44
Re: Chebyshev's InequalityOh! So inequality inside parenthesis in the probability arithmetic means sum of probabilities of all events which satisfy the inequality? I think this would be more clear. Don't you think? 