3. Let X1,X2 be jointly normally distributed with zero means, unit variances, and correlation coefficient . Let

3. Let X1,X2 be jointly normally distributed with zero means, unit variances, and correlation coefficient ρ. Let S be a χ2(n) RV that is independent of (X1,X2). Then the joint distribution of Y1 = X1/

(

S/n and Y2 = X2/

(

S/n is known as a central bivariate t-distribution. Find the joint PDF of (Y1,Y2) and the marginal PDFs of Y1 and Y2, respectively.