Conditional Expectations

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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
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Discrete Bivariate Distributions
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Example - Television Sales
Counts (Top Table) - JointMarginal Probabilites
(Bottom Table)
4
Example - Television Sales
Conditional Probabilities of Price Given Size
Conditional Probabilities of Size Given Price
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Functions of Discrete Bivariate R.V.s
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Example - Television Sales
Conditional Mean and Variance of Prices for Size
15.5
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Example - Television Sales
Conditional Mean and Variance of Price for all
Sizes
Note that the last column is the marginal
distribution of sizes
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Rules for Conditional Expectations
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Example - Television Sales
Marginal Distribution of Prices with Mean and
Variance
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Example - Television Sales
Means and Variances of Conditional Distributions
and Probabilities
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Example - Television Sales