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.279-288

Discrete Bivariate Distributions

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

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

Functions of Discrete Bivariate R.V.s

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

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

Rules for Conditional Expectations

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

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

Example - Television Sales