Assume 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 constant, and W is a noise term. Suppose V and W are independent and normally distributed with means 0 and variances of v and w.
a) Find Corr(S,V)
b) Given that S=s, what is the distribution of V?
c) What is the best estimate of V given S=s?
d) If this estimate is used repeatedly for different values of S coming from a sequence of independent values of V and W with the given normal distributions, what is the long-run average absolute value of the error of estimation?