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Therefore, the final prediction for the dark rate of the SiPM:
Therefore, the final prediction for the dark rate of the SiPM:
Dark Rate = <math>e^{-(1.12*1.6*10^{-19})/(1.381*10^{-23}*T)}</math> * 0.0033 mm^3 * 200 pixels * 2.329g/1000mm^3 * 6.022*10^23molecules/28g * <math>sqrt{2E_f/M_e} / Mean Free Path</math>
Dark Rate = <math>e^{-(1.12*1.6*10^{-19})/(1.381*10^{-23}*T)}</math> * 0.0033 mm^3 * 200 pixels * 2.329g/1000mm^3 * 6.022*10^23molecules/28g * (<math>sqrt{2E_f/M_e}</math>) / Mean Free Path
The data was then compared to a predicted dark rate of the device to determine the reliability of the prediction.
The data was then compared to a predicted dark rate of the device to determine the reliability of the prediction.
A <math>X^2</math> goodness of fit test was performed to determine how close the predicted dark rate came to the actual dark rate.
A <math>X^2</math> goodness of fit test takes the
<math>Sum{(Actual Value - Expected Value)^2/ Expected}</math>
If the value of the test statistic is aproximatly equal to the number of data points that were tested, then the equation determind above is a good predictor of the data; showing that the equation above is a good predictor of the dark rate of the SiPM used in the experiment.