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

Investigating the Probability Associated with the sums of k-independent digits of positive integers(k>2) as random variables

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=y_i) and cumulative probabilities, P(Y≤y_i) are valuables for inclusion in Standard Statistical Tables both for use by Students and Researchers.