1. Math 4030 – 6a Joint Distributions (Discrete)
Marginal and conditional
Independency
Properties of Mean and Variance

2. Joint (Probability) Distribution (Sec. 5.10):
f(x,y) x1 x2 … y1
f(x1,y1)
f(x2,y1) y2
f(x1,y2)
f(x2,y2) 1

3. Marginal probability and distributions:
f(x,y) x1 x2 … Y y1
f(x1,y1)
f(x2,y1) y2
f(x1,y2)
f(x2,y2) X 1

4. Conditional probability and distributions:

5. Random variables X and Y are independent if and only if
For all x and y!

6. Means:

7. Variances:

8. Covariance:
If X and Y are independent, then the covariance equals zero.

9. Properties of Means: Linearity: Mean of g(X) in general:
Variance as a special case when

10. Properties of Variance:
If X and Y are independent!