selected card's upper side . If this side is green, what is the probability that the other side of the card is also green? 3. (25 pts) Given a set of i.i.d samples X 1, ..., X,: Uniform (0, 0), find the maximum likelihood estimator of 0. (a) Write down the likelihood function. (10 pts) (b) Find the maximum likelihood estimator. (15 pts) 4. (10 pts) We are interested here in a particular 1-dimensional linear regression problem . The dataset corresponding to this problem has n examples (x1; yi), ...,(Xn; yn) where x; and y; are real numbers for all i. Let w* = [?;,?;]] be the least squares solution we are after . In other words , w minimizes J(?) = -[( , You can assume for our purposes here that the solution is unique 3|Page