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lected charged-current sample which contains very little neutral-current background. For both samples, the data points are seen to fall within or near the 1 standard de- viation range of the systematic uncertainty of the Monte Carlo simulation. 

The predictions of the energy spectra of the neutral- current and charged-current samples at the far-detector are based on the observed near-detector data and make use of the expected relationship between the neutrino fluxes at the two sites. The process of making the pre- dictions is called “extrapolation” and may be viewed as making corrections to the simulation of interactions in the far-detector based on the energy spectrum measured in the near-detector. 

This analysis uses an extrapolation technique called 

## V. FAR-DETECTOR PREDICTION 

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the “far over near” (F/N) method [4, 30]. This method makes the prediction of the far-detector spectrum by tak- ing the product of two quantities. The first quantity is the ratio of the expected number of events from the Monte Carlo simulation for each energy bin in the far- detector and near-detector spectra. The expected num- ber of events for each energy bin in the far-detector spec- tra depends on the composition of event types entering the samples and the corresponding oscillation probabili- ties for that energy. The second quantity is the number 

