Investigating Probability Distribution Associated with the Sum of at least Two Independent Positive Integers

Abstract

This work examined the probabilities associated with the sum of at least two positive integers. Let Y equals the sum of independent positive integers be a random variable. The histograms, probability density function (pdf) and the cumulative probabilities of Y were examined. Besides, the skewness and kurtosis were estimated to be zero (0) and approximately three (3) respectively. The distribution of Y showed clearly bell-shaped curves. Furthermore, the parameters of normal variable Y for at least two positive integers exhibited linear relationship. With these accomplishments it becomes feasible to simulate non-negative normal data sets within certain range of observations available for utilization in further Statistical research intending to mimic real life problems and phenomena. The calculated probabilities, P(Y=yi) and cumulative probabilities, P(Y≤yi) are valuables for inclusion in Standard Statistical Tables both for use by Students and Researchers.