Analysis reveals simplified moment generating function and probability density function of sample covariance, indicating importance of conditional distributions.
Both the Moment Generating Function and the Probability Density Function of sample covariance based on a bivariate normal distribution have been presented in a simpler way by using conditional distributions. We also prove that the random variable sample covariance is a linear combination of two chi-square random variables if they are statistically independent. Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 99-106
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Joarder et al. (2025) studied this question.
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