Hoeffding's Inequality Probability $>1$












0












$begingroup$


in one of the courses the professor said that Hoeffding's Inequality equation is this
enter image description here
but for me that does not make any sense as it can be greater than $1.$



For example, assume



$$varepsilon = 0.00001$$



$$N = 1000$$



That will make the probability $leq 2( e^{-2cdot 0.0000000001cdot 1000}) = 2cdot 0.999999 = 1.99999.$



Is there something wrong here?










share|cite|improve this question











$endgroup$

















    0












    $begingroup$


    in one of the courses the professor said that Hoeffding's Inequality equation is this
    enter image description here
    but for me that does not make any sense as it can be greater than $1.$



    For example, assume



    $$varepsilon = 0.00001$$



    $$N = 1000$$



    That will make the probability $leq 2( e^{-2cdot 0.0000000001cdot 1000}) = 2cdot 0.999999 = 1.99999.$



    Is there something wrong here?










    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      in one of the courses the professor said that Hoeffding's Inequality equation is this
      enter image description here
      but for me that does not make any sense as it can be greater than $1.$



      For example, assume



      $$varepsilon = 0.00001$$



      $$N = 1000$$



      That will make the probability $leq 2( e^{-2cdot 0.0000000001cdot 1000}) = 2cdot 0.999999 = 1.99999.$



      Is there something wrong here?










      share|cite|improve this question











      $endgroup$




      in one of the courses the professor said that Hoeffding's Inequality equation is this
      enter image description here
      but for me that does not make any sense as it can be greater than $1.$



      For example, assume



      $$varepsilon = 0.00001$$



      $$N = 1000$$



      That will make the probability $leq 2( e^{-2cdot 0.0000000001cdot 1000}) = 2cdot 0.999999 = 1.99999.$



      Is there something wrong here?







      probability






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      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 23 '18 at 6:06









      Gaby Alfonso

      972317




      972317










      asked Dec 23 '18 at 2:48









      asmgxasmgx

      1587




      1587






















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          $begingroup$

          Nothing is wrong - if the right hand side is greater than $1$, it just means that the inequality is pointless in that case, since all probabilities are less than or equal to $1$.






          share|cite|improve this answer









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            active

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            $begingroup$

            Nothing is wrong - if the right hand side is greater than $1$, it just means that the inequality is pointless in that case, since all probabilities are less than or equal to $1$.






            share|cite|improve this answer









            $endgroup$


















              2












              $begingroup$

              Nothing is wrong - if the right hand side is greater than $1$, it just means that the inequality is pointless in that case, since all probabilities are less than or equal to $1$.






              share|cite|improve this answer









              $endgroup$
















                2












                2








                2





                $begingroup$

                Nothing is wrong - if the right hand side is greater than $1$, it just means that the inequality is pointless in that case, since all probabilities are less than or equal to $1$.






                share|cite|improve this answer









                $endgroup$



                Nothing is wrong - if the right hand side is greater than $1$, it just means that the inequality is pointless in that case, since all probabilities are less than or equal to $1$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Dec 23 '18 at 2:53









                pwerthpwerth

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