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The actual energy of electrons follow a poisson distribution, where a large number of electrons have very little amounts of energy while a miniscule number of electrons have a very large amount of energy.  
 
The actual energy of electrons follow a poisson distribution, where a large number of electrons have very little amounts of energy while a miniscule number of electrons have a very large amount of energy.  
Therefore, the probability of the electionhaving a large amount of energy is
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Therefore, the probability of the elections having a large amount of energy is
    
<math>Probability = e^{-E_g/kT}</math>
 
<math>Probability = e^{-E_g/kT}</math>
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