You are contemplating investing in a particular stock tomorrow and one of your brokers believes there is a 40% chance that the stock will increase over the next few weeks, a 20% chance that the price will be essentially unchanged, and a 40% chance that the price will decline. You ask another broker and she gives you 35%, 30%, and 35%, respectively, for the three possible outcomes. Assume that you accept these percentages. If X = the outcome under the first broker’s judgment and Y = the outcome under the second broker’s judgment, which random variable has the smaller variance? What course of action would you follow?
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