Let me know right away if you find any obvious errors in this solution set. To get you up to speed, this problem set highlights some of the concepts you should have grasped in your prerequisite coursework. The first three or four lectures will be devoted to a thorough, although quick, review of this material. This problem set covers material in Gujarati, Chapter 2. 1. We will be using summation notation in this course.
Correlation is a measure of the degree of linear relatedness of two variables.
Two variables may display a very rigid relationship that is nonlinear , so that correlation will be zero. Consider, for example, two variables for which a scatterplot looks like a perfect circle. Their correlation will be zero, but they definitely bear a systematic relationship. This is not a complete probability distribution because for the entire distribution to be described, the sum of the probabilities must be one. This means that each probability is between zero and one, and the sum of the probabilities is unity.