1. Conditional Expectations
Bivariate Probability Distributions
Discrete Case - Television Sales Data
Data Source: Benson (1966): “Analysis of Irregular Two-Dimensional Distributions of Consumer Buying Choices”, Journal of Marketing Research, Vol. 3, #3, pp

2. Discrete Bivariate Distributions

3. Example - Television Sales
Counts (Top Table) - Joint&Marginal Probabilites (Bottom Table)

4. Example - Television Sales
Conditional Probabilities of Price Given Size
Conditional Probabilities of Size Given Price

5. Functions of Discrete Bivariate R.V.s

6. Example - Television Sales
Conditional Mean and Variance of Prices for Size = 15.5

7. Example - Television Sales
Conditional Mean and Variance of Price for all Sizes
Note that the last column is the marginal distribution of sizes

8. Rules for Conditional Expectations

9. Example - Television Sales
Marginal Distribution of Prices with Mean and Variance

10. Example - Television Sales
Means and Variances of Conditional Distributions and Probabilities

11. Example - Television Sales