1. Suppose that Yi = β0 + β1Xi + i, where ei is N(0, 0.3), β0 = 1.4, and β1 = 1.7.  (a) What are the conditional mean and standard deviation of Yi given that Xi = 1? What is P(Yi ≤ 3|Xi = 1)?  (b) A...

1. Suppose that Yi = β0 + β1Xi + i, where ei is N(0, 0.3), β0 = 1.4, and β1 = 1.7.

 (a) What are the conditional mean and standard deviation of Yi given that Xi = 1? What is P(Yi ≤ 3|Xi = 1)?

 (b) A regression model is a model for the conditional distribution of Yi given Xi. However, if we also have a model for the marginal distribution of Xi, then we can find the marginal distribution of Yi. Assume that Xi is N(1, 0.7). What is the marginal distribution of Yi? What is P(Yi ≤ 3)?