Quiz 1

Quiz 1 (12 minutes)

Suppose the joint distribution of \(\left(X_1,v\right)\) is bivariate normal, i.e., \[\left(\begin{array}{c} X_{1}\\ v \end{array}\right)\sim N\left(\left(\begin{array}{c} 1\\ 0 \end{array}\right),\left(\begin{array}{cc} 4 & 3\\ 3 & 9 \end{array}\right)\right). \] A random sample \(\{\left(X_{1t},v_t\right)\}\) was obtained from this joint distribution and \(Y_t\) was obtained by \(Y_t=2+3X_{1t}+v_t\).

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Another version of the quiz (12 minutes)

Suppose the joint distribution of \(\left(X_1,v\right)\) is bivariate normal, i.e., \[\left(\begin{array}{c} X_{1}\\ v \end{array}\right)\sim N\left(\left(\begin{array}{c} \mu_1\\ 0 \end{array}\right),\left(\begin{array}{cc} \sigma^2_1 & \sigma_{1v}\\ \sigma_{1v} & \sigma^2_v \end{array}\right)\right). \] A random sample \(\{\left(X_{1t},v_t\right)\}\) was obtained from this joint distribution and \(Y_t\) was obtained by \(Y_t=\beta_0+\beta_1X_{1t}+v_t\).