Documents / Report
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.
“Works”7 pages
UNCLASSIFIED//FQA: QFFI&l11J.k W&liii Q•lklf fN( 11 ,muc)= ~ ✓ 27r u e -.u . e 2 (82) This is "hhw likely" the mhst likely number of ExtraTerrestrial Civilizatiom in the Galaxy is, i.e. it is the peak height ill the fognonnal probability density Junction fv (11). Next to the mode. the median m (ref. [9]) is one more statistical number u~ed to characterize any probability distribution. It 1s defined a~ the independent variable ah~cissa m ~uch that a rcalizati(]n of the random variable will take up a value lower than 111 with 50% probability or a value higher than m with 5W/r probability again. In other wonh. the median m splits up our prohahility den~ity in exactly two equally probable parts. Since the probability of occurrence of the random event cquab the area under its demity rurve (i.e. the definite integral under its density curve) then the median 111 (of the lognormal distribution. in this case) is defined as the integral upper limit m: lln(11f-1,l· 2c,· 2 (83) In order to find m, we may 1101 differentiate (83) with respect to Ill , since the ··precise'" factor './i on the right would then di~appear into a zero. On the rontrary, we may try to perform the obvious suh~titution (in(,,)-μ)' 2 ()2 (84) into the integral (83) to reduce it to the fulluwing integral defining the error function crf(;:) Random variable Probability distribution Probability density function Mean value Variance Standard deviation 42 (85) Then, after a few rcduetiom that we skip for the sake of brevity, the full cquatiun (83) is turm;d intu that i~ ,,rf[ln(m)-;,)~o ✓2a (86) (87) Since from the defimtion (85) one obviously has erf(0J=0. (87) becomes whence finally ln(m)-p=O ✓2a Irredian = 111 = e.u I. (88) (89) This is the median of the log11ormaf distribution of N. In other words, this is the 1111mber of ExtraTerrestrial civiliza1io11s i11 1he Galaxy such that, with 50% probability the acmal value of N will be lower tha11 this media 11, a11d with 50% probabili1y it will be higher. In conclusion, we feel useful to summarize all the equations that we derived about the random variable N in the following Table 2. N = number of communicating ET civilizations in Galaxy Lognormal /Jn/111--.uJ'- fN(n)=I.. I lu' (II?'. 0)---, n 5u "- (N)~,,"c' , a,\, 'p a'(a' i)= e- e e -1 a' a,.v =cl-'e 2 Jerr' -1 UNCLASSIFIED/ }FQA: QFFiliIAk .. !iii 8HLV
Not linked to a story yet.
Report, from the dia collection. The PDF is mirrored here; the original link is under it. 55 pages are in the text index: search them above, or from the library's search.