All the new concepts covered since Midterm 11 The joint pdf

All the \"new\" concepts covered since Midterm 1-1] The joint p.d.f. for two random variables, X and Y, is defined as when this derivative exists. Suppose that random variables X and Y have a joint, p.d.f. Determine the marginal p.d.f.\'s f_X(x) and f_Y(y) for X and Y. Find the average, or mean, value of each of the random variables, Find the variance of each of the random variables, Find the covariance, between X and Y. Find the correlation coefficient between X and Y, Find an expression for the minimum mean square error linear estimator of Y given X = x. The result will be of the form where a and b minimize Determine whether X and Y governed by f_XY of Eqn. (3) are statistically-independent random variables. What does the condition on F_XY(x,y) imply about f_XY(x,y) in the case of statistically-independent random variables? The answer is apparent from the definition in Eqn. (2). Show that the joint c.d.f. for X and Y is given by

Solution