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Abstract
Polymerase chain reaction (PCR) is a popular method of detecting the presence of a target gene. A mathematical model is developed based upon the principals of branching processes and confidence intervals for various methods of determining a probability of reproduction are given. The model is tested using simulations based upon the stochastic process of PCR. The model proves to be a valid and useful method for determining the initial copy number of a target, regardless of the size of the copy number.