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I am having an interesting discussion on a newsgroup (alt.assassination.jfk) regarding the single bullet theory (SBT) from the JFK assassination. The problem with the SBT is that it conflicts with much of the evidence.
The current SBT to which most SBT adherents subscribe (e.g Gerald Posner in his book Case Closed) has the first shot missing the limo and its occupants entirely at time t=160 and the second shot hitting both JFK and Gov. Connally at time t= 224 (each unit is one frame of the Zapruder film which were taken at 18.3 frames/second). During this period from t=160 to t=196 JFK is smiling and waving to the crowd. From t=197-207 he still has his hand up but is looking forward and the facial features are blurred. From t=207 to t=224 he is behind a road sign and not visible to Zapruder's camera.
The problem is that there are at least 17 witnesses by my count (their evidence is compiled http://www.dufourlaw.com/jfk/first_shot_hit_witnesses.PDF" ) who said that JFK reacted to the first shot. Most said he moved to the left and brought his hands to his neck but NONE said he kept smiling and waving to the crowd.
Also, the shot pattern according to this SBT is 1...2...3, the space between the first two being about 64 frames and between the last two 99 frames. However, the witnesses heard a quite different shot pattern with the last two shots closer together. I have compiled their evidence http://www.dufourlaw.com/jfk/shot_pattern_evidence.pdf".
Now, without knowing anything about the reliability of these witnesses I say that the convergence cannot reasonably happen by chance.
With respect to the 17 witnesses to 0 who said that JFK reacted to the first shot, let's say that the odds were 1/2 that any witness would get this observation wrong (quite apart from the odd fact that they all thought he reacted in the same or very similar way). The chance that in 17 witnesses you would not find one witness who said that JFK kept smiling and waving after the first shot is [itex]p = 1/2^17 = 1/131072[/itex]. And that, as I say, assumes that the witnesses were only 50% reliable.
With respect to the 44 witnesses who recalled the 1...2...3 pattern versus the 6 who thought the pattern was 1...2...3, which could fit the SBT, let's say the probability of getting this right was 50%. Then the probability of 44 of the 50 witnesses hearing one pattern over the other is given by a simple binomial distribution function:
[tex]f_p(44) = \frac{50!.5^{50}}{44!6!}[/tex]
which works out to 1.4 x 10-8. For these conditions, the mean number of events is 25 and the standard deviation is 3.5.
This tells me that the witnesses are reliable because our assumption that they were not reliable gives a result that is extremely improbable. Am I wrong?
AM
The current SBT to which most SBT adherents subscribe (e.g Gerald Posner in his book Case Closed) has the first shot missing the limo and its occupants entirely at time t=160 and the second shot hitting both JFK and Gov. Connally at time t= 224 (each unit is one frame of the Zapruder film which were taken at 18.3 frames/second). During this period from t=160 to t=196 JFK is smiling and waving to the crowd. From t=197-207 he still has his hand up but is looking forward and the facial features are blurred. From t=207 to t=224 he is behind a road sign and not visible to Zapruder's camera.
The problem is that there are at least 17 witnesses by my count (their evidence is compiled http://www.dufourlaw.com/jfk/first_shot_hit_witnesses.PDF" ) who said that JFK reacted to the first shot. Most said he moved to the left and brought his hands to his neck but NONE said he kept smiling and waving to the crowd.
Also, the shot pattern according to this SBT is 1...2...3, the space between the first two being about 64 frames and between the last two 99 frames. However, the witnesses heard a quite different shot pattern with the last two shots closer together. I have compiled their evidence http://www.dufourlaw.com/jfk/shot_pattern_evidence.pdf".
Now, without knowing anything about the reliability of these witnesses I say that the convergence cannot reasonably happen by chance.
With respect to the 17 witnesses to 0 who said that JFK reacted to the first shot, let's say that the odds were 1/2 that any witness would get this observation wrong (quite apart from the odd fact that they all thought he reacted in the same or very similar way). The chance that in 17 witnesses you would not find one witness who said that JFK kept smiling and waving after the first shot is [itex]p = 1/2^17 = 1/131072[/itex]. And that, as I say, assumes that the witnesses were only 50% reliable.
With respect to the 44 witnesses who recalled the 1...2...3 pattern versus the 6 who thought the pattern was 1...2...3, which could fit the SBT, let's say the probability of getting this right was 50%. Then the probability of 44 of the 50 witnesses hearing one pattern over the other is given by a simple binomial distribution function:
[tex]f_p(44) = \frac{50!.5^{50}}{44!6!}[/tex]
which works out to 1.4 x 10-8. For these conditions, the mean number of events is 25 and the standard deviation is 3.5.
This tells me that the witnesses are reliable because our assumption that they were not reliable gives a result that is extremely improbable. Am I wrong?
AM
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