I have a doubt with regards to sample covariance.
The sample covariance between two random variables x & y can be given as $\frac{1}{N} \sum_i{(x_i - \mu_x)(y_i - \mu_y)}$ assuming the mean's $\mu_x \text{ and } \mu_y$ are known. However if the means are known we estimate the sample means and have the new covariace as $\frac{1}{N-1} \sum_i{(x_i - \mu_x')(y_i - \mu_y')}$ where $\mu_x'$ and $\mu_y'$ are means computed from the data itself. The $(N-1)$ term accounts for Bessel's correction.
My question is what happens when we know exactly one mean of the two random numbers i.e $\mu_x$ or $\mu_y$ is exactly known and need not be computed from the data. What would be the correction term now?