Probability - the telephone directory problem - AnalyticBridge 2019-06-18T05:12:27Z https://www.analyticbridge.datasciencecentral.com/forum/topics/2004291:Topic:8188?feed=yes&amp%3Bxn_auth=no Hi Raman, Are you assuming t… tag:www.analyticbridge.datasciencecentral.com,2008-03-25:2004291:Comment:8575 2008-03-25T18:01:45.710Z John Hughes https://www.analyticbridge.datasciencecentral.com/profile/JohnHughes Hi Raman,<br /> <br /> Are you assuming that the number 'm' is an idealised natural number and so the probability distribution of each digit is from the General Significant-Digit Law derived in T Hill. The Significant-Digit Phenomenon. The American Mathematical Monthly 102, 322-327 (1995). This distribution explains Benford's Law and is:<br /> <br /> _m_<br /> \ m-i<br /> p(D1,D2 ... Dm) = log10(1 + \ di x 10 )<br /> /<br /> /___<br /> i=1<br /> <br /> The General Sigificant-Digit Law has the surprising corollary that significant digits are… Hi Raman,<br /> <br /> Are you assuming that the number 'm' is an idealised natural number and so the probability distribution of each digit is from the General Significant-Digit Law derived in T Hill. The Significant-Digit Phenomenon. The American Mathematical Monthly 102, 322-327 (1995). This distribution explains Benford's Law and is:<br /> <br /> _m_<br /> \ m-i<br /> p(D1,D2 ... Dm) = log10(1 + \ di x 10 )<br /> /<br /> /___<br /> i=1<br /> <br /> The General Sigificant-Digit Law has the surprising corollary that significant digits are dependent.<br /> <br /> Thanks<br /> <br /> John Hi Raman, I'm assuming that… tag:www.analyticbridge.datasciencecentral.com,2008-03-25:2004291:Comment:8572 2008-03-25T17:53:53.557Z John Hughes https://www.analyticbridge.datasciencecentral.com/profile/JohnHughes Hi Raman,<br /> <br /> I'm assuming that the number 'm' is an idealised natural number and so the probability distribution of each digit is from the General Significant-Digit Law derived in Theodore Hill's paper The Significant-Digit Phenomenon. The American Mathematical Monthly 102, 322-327 (1995). This distribution is:<br /> <br /> _m_<br /> \ m-i<br /> p(D1,D2 ... Dm) = log10(1 + \ di x 10 )<br /> /<br /> __ Hi Raman,<br /> <br /> I'm assuming that the number 'm' is an idealised natural number and so the probability distribution of each digit is from the General Significant-Digit Law derived in Theodore Hill's paper The Significant-Digit Phenomenon. The American Mathematical Monthly 102, 322-327 (1995). This distribution is:<br /> <br /> _m_<br /> \ m-i<br /> p(D1,D2 ... Dm) = log10(1 + \ di x 10 )<br /> /<br /> __