Imagine that you are trying to predict the price of gasoline (regular unleaded) and the price of natural gas for home heating during the next month. Assume you believe that the price of either will stay the same, go up by 5%, or go down by 5%. Assess the joint probabilities of these possibilities, that is, assess nine probabilities that sum to 1 and are “realistic.” Do you believe it is easier to assess the marginal probabilities of one and the conditional probabilities of the other, or to assess the joint probabilities directly?
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