The simples approach is:

1. Calculate average counts number per single channel for both, lower and upper background areas.

2. Make average of the two just calculated numbers - that's the average background (per channel) for all the peak region.

3. Multiply number from point 2 by number of channels in the peak - that's background of your peak. Subtract this number from total counts for the peak to get the peak net counts.

4. peak uncertainty = sqrt(peak net)

5. background uncertainty = sqrt(bacground counts - see point 3)

6. detection limit is usually defined: If measured peak (net) is bigger than 3*standard uncertainty of bacground it can be assummed as detected peak.

This gives that peak net should be greater than 3*sqrt(bacground) to be accounted as real peak and not backround fluctuation.

However to be able to quantify the analyte the peak should be greater than 3*detection limit calculated as above.

Some more details e.g here:

http://www.nucleide.org/ICRM_GSWG/Workshop_2009/03_Tuesday_morning/01.%20De%20Felice%20LD%20MDA.pdf

Thank you very much

G.F.Knoll 'Radiation Detection and measurement' the first chapter about statistics might give you the background