- * diff(logL, mu1) = -(mu1 - mu2 - x) / sigma_c^2
- * maximizer for mu1 is given by: sum_i[ (1/sigma_c_i)^2 (mu1 - mu2_i - x_i) ] = 0
- * sum_i[ (1/sigma_c_i)^2 mu1 ] = sum_i [ (1/sigma_c_i)^2 ( mu2_i + x_i ) ]
- * mu1 = sum_i [ (1/sigma_c_i)^2 ( mu2_i + x_i ) ] / sum_i[ (1/sigma_c_i)^2 ]
+ * diff(logL, mu1) = -w * (mu1 - mu2 - x) / sigma_c^2
+ * maximizer for mu1 is given by: sum_i[ (w_i/sigma_c_i)^2 (mu1 - mu2_i - x_i) ] = 0
+ * sum_i[ (w_i/sigma_c_i)^2 mu1 ] = sum_i [ (w_i/sigma_c_i)^2 ( mu2_i + x_i ) ]
+ * mu1 = sum_i [ (w_i/sigma_c_i)^2 ( mu2_i + x_i ) ] / sum_i[ (w_i/sigma_c_i)^2 ]