Question: Suppose that the magnitude of a signal received from a satellite is
S= α + bV +W
Where V is a voltage which the satellite is measuring, α and b are constants, and W is a noise term suppose V and W are independent and normally distributed with means 0 and variances σv2 and σw2.
a) Find Corr(X, V).
b) Given that S = si 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?