Suppose I have independent variables $X$ and $Y$ which follows exponential distribution with parameter $\lambda$. I want to find the variance of correlation estimator $\hat{\rho}$ which is defined as: $$ \hat{\rho} = \frac{\sum_{i=1}^{n} x_i y_i}{\sqrt{\sum_{i=1}^{n}x_i^2 \sum_{i=1}^{n}y_i^2}} $$ Since it involves a division I couldn't even start calculating the variance. How can I do it?
2026-03-27 01:14:01.1774574041
correlation estimator
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