Define a general trivariate normal distribution with suitable parameters. Obtain the conditional distribution of (X1, X2) given X3 = x3 and an expression to compute the partial correlation coefficient between (X1, X2) after controlling the effects of X3. Also, obtain the regression function of X1 on X2 and X3 alongside the expression for the squared multiple correlation coefficient between X1 and the combined effect of (X2, X3).
