Radioactive measurements in the decay process of any radioactive sample can be predicted by radioactive-decay law. This predication is based over its average behavior. In actual practice, the radioactive measurements show fluctuations about the average value. For any radioactive sample, there is an exact number which disintegrates in any given unit of time fluctuates around the average value. In counting applications, it is important to estimate this fluctuation because it indicates the repeatability of results of a measurement. This will identify it by using periodogram analysis that depicts the periodicity in the radioactive decay of the given sample of Americium-241. Statistical distributions that the given sample followed with goodness-of-fit tests are examined. Maximum-Likelihood Estimator (MLE) has been used to find the population parameters. The randomness in radioactive decay has been verified by non-parametric method. These statistical analyses are based over the amount of internal fluctuation in the given radioactive source that is consistent with the predictions obtained. These measurements are obtained by measuring the decay of 300 counts per 10 sec. of Americium-241 using a Geiger Muller (GM) Counter in the teaching laboratory, at the | department of Physics, University of Karachi, Karachi, Pakistan.
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