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.
UNCLASSIFIED/,'f81il 8fflll... k WliEii SUlklf
ref. [51. The advantage of this notation is that it
makes a neat distinction between probabilistic (or
statistical: it's the same thing here) variables,
ahvays denoted by capital.~, from non-probabilistic
(or "dctcm1inistic") iariablcs. always denoted by
lower-case letter\. Adopting the Papoulis notation
also is a tribute lo him by this author. who wa, a
Fulbright Grantee in the United States with him at
the Polytechnic Institute (now Polytechnic
University) of New York in the years I 977-78-79.
We thu~ introduce seven new (po~itive)
random variables D, ("rr from "'Drake") defined
as
j~:: ::D_1 =ne
D4 -= fl
D'i = ji
Dh =F
/J7 = fL
(2)
~o 1hat uur STATISTICAL Drake equation may be
~imply rewritwn as
30
(3)
Of course. N now becomes a (positive) random
variable too. having its own (positive) mean value
and ~tandard deviation. Ju~t as each of the D, has its
nwn (po~i!ivc) mean \'Hlue and standard dc\·iatinn ..
. . . the natural quest inn then arises: how arc the sci en
mL:an ialucs un thL: right rdatL:d HI 1hc mrnn ialue on
the left?
and how are the seven standard deviations on the
right related to the standard deviation on the left'!
Just take the next step.
3. STEP 2, INTRODUCING LOGS TO
CHANGE THE PRODUCT INTO A SUM
Prm.luc1s uf random variable~ arc 1101 ca~y HI
handk in prubabili1y theory. h is actually much
L:asicr HI handk sums of random variables, rathL:r
than prnducts, because:
l) The probability dcnsi1y uf the sum uf two or
more independent random variables i~ the
rnnvolution of the relevant probability
den~itie~ (wony not about the equations,
right now).
2) The Fourier transform of the convolution
~imply i~ the produL:t of the Fourier
transforms (again, worry not about the
equations, at this point)
UNCLASSIFIED//COP AFFJCJC k Wlii 8HLV Not linked to a story yet.
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.