On the moments of sample covariance from a bivariate normal population

The distribution of the sample covariance based on a sample from a bivariate normal population has been derived in the literature by many authors. Some used conditionality principle, some used inverse Mellin transform and some used simple transformations. The main contribution of the paper is the direct derivation of the general moment structure of sample covariance via a lemma dealing with a infinite sum of product of two gamma functions. Integer valued moments of any order are also derived in terms of hypergeometric function. Some corollaries have been deduced which have potential for further use in mathematics and statistics. The probability density function, skewness and kurtosis have been graphed.