1 Def: Let and be random variables of the discrete type with the joint p.m.f. on the space S. (1) is called the mean of (2) is called the variance of (3) is called the covariance of

2 (4) is called the correlation coefficient of

3 Remark

4Remark Let X and Y be two discrete r.v.s, the correlation coefficient Y X

5 So, If pairs (x, y) in area I and III contain most of the probability of the distribution, the correlation coefficient will tend to be positive. On the other hand, if pairs (x, y) in area II and IV contain most of the probability of the distribution, the correlation coefficient will tend to be negative.

6 Estimation How to estimate these characteristic? By constructing functions of sample observations. For example mean Sample mean Variance --- Sample variance

7 Estimation Sample covariance

8 Estimation