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Extra resources for Measurement and Detection of Radiation, Third Edition
Sample text
13 hold for any number of events provided the events are mutually exclusive or stochastically independent. ,N P(x1 + x2 + . . + xN) = P(x1) + P(x2) + . . 14) P(x1 x2 . . xN) = P(x1) P(x2) . . 4 PROBABILITY DISTRIBUTIONS AND RANDOM VARIABLES When an experiment is repeated many times under identical conditions, the results of the measurement will not necessarily be identical. In fact, as a rule rather than as an exception, the results will be different. Therefore, it is very desirable to know if there is a law that governs the individual outcomes of the experiment.
Such a law, if it exists and is known, would be helpful in two ways. First, from a small number of measurements, the experimenter may obtain information about expected results of subsequent measurements. Second, a series of measurements may be checked for faults. If it is known that the results of an experiment obey a certain law and a given series of outcomes of such an experiment does not follow that law, then that series of outcomes is suspect and should be thoroughly investigated before it becomes acceptable.
In the example given above, if gammas of three different energies produce the pulses at the output of the preamplifier, the pulses at the output of the amplifier will be attributed erroneously to gammas of two different energies. To avoid such an error, an observer should follow this rule: Before any measurement of particle energy, make certain that the highest pulse of the spectrum to be measured is less than 10 V at the output of the amplifier. In addition to signal amplification, an equally important function of the amplifier is to convert the signal at the output of the preamplifier into a form suitable for the measurement desired.