Problem 21. Consider the following normal regression model: yz- :3 13.31 .,; where i~.i.d.N(0,02) (1) Do the following using R: a) Generate 100 observations of act- from the i.i.d. uniform distribution on the interval (0,20). b) Then, generate 100 observations of yi- using the (551-)! 5 drawn from a) wit-113 = 0.7 and drawing 100 observations of .5 with 0' = 1 C) Plot the data. And Plot the likelihood on the interval (0, 1) fort? Problem 22. This time, consider random variable Y with the following exponential distri bution: 1 _y 33(9) = ()f3 \"a Withy>UaE(Y) =#>0 (2) ,u, Suppose you have the following model for ,u; 2 BO\") : 30/111?) = g \"3 (3) a) Show that the likelihood for n independent realizations corresponding to 11 different ygs is given by: a w) = we imam2": M r} (4) 1