Problem 6 (10 pt and bonus)
In the context of the normal simple linear regression model Y = β0 + β1X + ε, let Yi be an observation corresponding to Xi. Find the 95th percentile of Y. (5 pt)
If X follows a standard normal distribution, find the joint probability density function of (X, Y). (Bonus pt)
Let z = -10. Find E(Z), Var(Z), and cov(X, Z).