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The distribution in the number of photons in the light pulses from the phosphor of a five dynode transmission secondary electron image intensifier (TSEM) has been measured for single photoelectrons emitted from the cathode. This distribution reflects the distribution in the secondary electron multiplication in the dynode structure. The distribution is monotonically decreasing, but deviates significantly from a simple exponential. The noise distribution has also been studied and several different components distinguished. The effects on these components of cooling the cathode has been investigated.