due to a variant of Bessel's correction: In short, the sample covariance relies on the difference between each observation and the sample mean, but the sample mean is slightly correlated with each observation since it is defined in terms of all observations. If the population mean is known, the analogous unbiased estimate using the population mean, has in the denominator. This is an example of why in probability and statistics it is essential to distinguish between random variables (upper case letters) and realizations of the random variables (lower case letters). The maximum likelihood estimate of the covariance for the Gaussian distribution case has N in the denominator as well. The ratio of 1/N to 1/(N − 1) approaches 1 for large N, so the maximum likelihood estimate approximately equals the unbiased estimate when the sample is large. Distribution of the sample mean For each random variable, the sample mean is a good estimator of the population mean, where a "good" estimator is defined as being efficient and unbiased. Of course the estimator will likely not be the true value of the population mean since different samples drawn from the same distribution will give different sample means and hence different estimates of the true mean. Thus the sample mean is a random variable, not a constant, and consequently has its own distribution. For a random sample of N observations on the jth random variable, the sample mean's distribution itself has mean equal to the population mean and variance equal to , where is the population variance. The arithmetic mean of a population, or population mean, is often denoted μ. The sample mean (the arithmetic mean of a sample of values drawn from the population) makes a good estimator of the population mean, as its expected value is equal to the population mean (that is, it is an unbiased estimator). The sample mean is a random variable, not a constant, since its calculated value will randomly differ depending on which members of the population are sampled, and consequently it will have its own distribution. For a random sample of n independent observations, the expected value of the sample mean is and the variance of the sample mean is If the samples are not independent, but correlated, then special care has to be taken in order to avoid the problem of pseudoreplication. If the population is normally distributed, then the sample mean is