  We report the observation of electroweak single top quark production in 3.2
fb-1 of ppbar collision data collected by the Collider Detector at Fermilab at
sqrt{s}=1.96 TeV. Candidate events in the W+jets topology with a leptonically
decaying W boson are classified as signal-like by four parallel analyses based
on likelihood functions, matrix elements, neural networks, and boosted decision
trees. These results are combined using a super discriminant analysis based on
genetically evolved neural networks in order to improve the sensitivity. This
combined result is further combined with that of a search for a single top
quark signal in an orthogonal sample of events with missing transverse energy
plus jets and no charged lepton. We observe a signal consistent with the
standard model prediction but inconsistent with the background-only model by
5.0 standard deviations, with a median expected sensitivity in excess of 5.9
standard deviations. We measure a production cross section of
2.3+0.6-0.5(stat+sys) pb, extract the CKM matrix element value
|Vtb|=0.91+0.11-0.11 (stat+sys)+-0.07(theory), and set a lower limit |Vtb|>0.71
at the 95% confidence level, assuming m_t=175 GeVc^2.
