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# Conditional Distribution

A company sells two products (Product 1 and Product 2) that tend to be substitutes for each other. That is, if a customer buys Product 1, she tends to not buy Product 2, and vice versa. The company assessed the joint probability distribution of demand for the two products for this year. The joint distribution is shown below. The left margin shows the possible demand amounts for Product 2 and the top margin shows the possible demand amounts for Product 1.

Using this information, we can check to see if these two products behave as partial substitutes.

a. Determine the conditional distribution of demand for Product 2 given that demand for Product 1 is 400. That is, given that demand for Product 1 is at its highest, what are the conditional probabilities for the different demand levels of Product 2?
b. Determine the conditional distribution of demand for Product 1 given that demand for Product 2 is 250.
c. Two products show signs of being substitutes if, when the demand for one product is high, that means the demand for the other product is likely to be low (that is, lower demand for the other product is more likely than higher demand). Do you see any patterns in the conditional probability distributions you calculated above?

#### Solution Preview

Please see the attached file.

a. Determine the conditional distribution of demand for Product 2 given that demand for Product 1 is 400. That is, given that demand for Product 1 is at its highest, what are the conditional probabilities for the different demand levels of Product 2?

P(B) is the sum of the following probabilities: 0.035+0.025+0.020+0.010+0.010 =0.1

So for each demand of product ...

#### Solution Summary

The solution gives detailed answers to the question below.

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