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The influence of pure statistical fluctuations on $K/\pi$ ratio isinvestigated in an event-by-event way. Poisson and the modified negativebinomial distributions are used as the multiplicity distributions since theyboth have statistical background. It is shown that the distributions of theratio in these cases are Gaussian, and the mean and relative variance are givenanalytically.Comment: 6 pages in RevTeX, 3 eps figures include

INFLUENCE OF STATISTICAL FLUCTUATIONS ON K/π RATIOS IN RELATIVISTIC HEAVY ION COLLISIONS