Problem 3. Suppose that the magnitude of a signal received from a satellite is S = a + bV + W where V is a voltage which the satellite is measuring, a and b are constants, and W is a noise term. Suppose V and W are independent and normally distributed with means 0 and variances of and Ow respectively. (a) Find the correlation between S and V. (b) Given that S = s, what is the distribution of V? (c) What is the best estimate of V given S = $7 (Hint: use conditional expectation.) (d) If this estimate is used repeatedly for different values of S coming from a sequence of inde- pendent values of V and W with the given normal distributions, what is the long-run average absolute value of the error estimation