bservations? 2. (10 points) In this exercise we derive the Bayesian connection to the Lasso. (a) Consider the following linear regression without an intercept: yi = where E1, . . ., En are independent and identically distributed as N(0, o2) and 02 is known. What is the likelihood for the data? [Hint: the density of the N(M, w2) distribution is P ( 2; 14, W2 ) = (2TW?) -ze- 202 (2-14)? (b) Assume the following prior for B: B1, . .., Bp are independent and identically distributed as double exponential random variables with density function P(B) = II e-18;1/T j=1 Using the Bayes' Theorem, derive the posterior for B. (c) By choosing T appropriately, show that the mode of the posterior distribution p(B | y) is the same as the Lasso estimate. [Hint: the value of z that maximizes f(z) is the same as the value of z that minimizes - f(z).]