Let X and Y be random variables with respective means X and Y , respective variances 2 X

QUESTION:

Let X and Y be random variables with respective means \(\mu_X\) and \(\mu_Y\), respective variances \(\sigma^2_X\) and \(\sigma^2_Y\), and correlation coefficient \(\rho\). Fit the line y = a + bx by the method of least squares to the probability distribution by minimizing the expectation

               \(K(a, b) = E[(Y − a − bX)^2]\)

with respect to a and b. Hint: Consider \(\partial K/\partial a = 0\) and \(\partial K/\partial b = 0\), and solve simultaneously.