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This Defense Intelligence Agency reference document, dated 11 March 2010, is one of the advanced technology reports produced in FY 2009 under the Advanced Aerospace Weapon System Applications (AAWSA) program. It introduces the Statistical Drake Equation, which replaces each factor of Frank Drake's 1961 equation with a uniform random variable to estimate how far away the nearest extraterrestrial civilization is. In the worked example, there is a 75% probability that the nearest civilization lies between 1,361 and 3,979 light years from Earth.
“The Advance”6 pages
UNCLASSIFIED//F&~ 8FFI&I.«1k WliEii SUlklf Appendix A: Proof of Shannon's 1948 Theorem Stating That the Uniform Distribution is the "Most Uncertain" One Over a Finite Range of Values Information Theory was initiated by Claude Shannon (1916-2001) in his well-known 1948 two papers: F.~,-.::.:~:I w,:h :o,:•:c_i'.'lJ.c ~o:t I'e,. lS-3 A :\farhenrnrical Theo1'\" of Communication In this Appendix, we wish to draw attention to a couple of theorems that Shannon proves on pages 36 and 37 of his work, and read, respectively (note that Shannon omits the upper and lower limits of all integrals in the first theorem: they are minus infinity and plus infinity, respectively): and 25 5. Let p:x1 be a cue-duueu',1oual d:;r11'::mh011 :iie :'ouudp -'-' g:in:1g a lilllXmmmeutr::,py -;ub_1ec1 to tlle :-:nditi2'Il tha: fae <_,fJ.nd.ud des:ic1t1cn -:f x be fi.;:ed :it ,, 1,, Gc1a;<_,1ctu. TL, <_,h-:-•.,· thi,, 1.\"e mu',! 111.1..';:lllllZe " ••• I.\ - /p-:.,·1logp :r:,h ·.nth .,,· - / p,,.-,.,_:d:r and : - ./ p x1d:r ct', c::i:F,ttam:-;. Thi,, requm~-,. by :he calmlu-, -:-f,:an<1t101r,. m<1x1llllzmg :be c::indtttoa !01 tluc. i; kg_:.•."_\I. ,\_l_'~ - /I - (I UNCLASSIFIED/ ,'f811. 8ffll!l"L 1!181! 911L f
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Report, from the dia collection. The PDF is mirrored here; the original link is above. 55 pages are in the text index: search them above, or from the library's search.