I'm reading Modern Mathematical Statistics with Applications and I don't know how to get the covariance of $\rho$ from $X$ and $Y$ in Example 6.16:
Where do I start?
2026-03-26 12:35:27.1774528527
Calculate covariance of two bivariate normal random variables
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Use linearity of covariance. \begin{align} \operatorname{Cov}(X,Y) &= \operatorname{Cov}(Z_1, \rho Z_1 + \sqrt{1-\rho^2} Z_2) \\ &= \rho \operatorname{Cov}(Z_1, Z_1) + \sqrt{1-\rho^2} \operatorname{Cov}(Z_1, Z_2). \end{align} Can you finish from here?