(a) For real applications, the normal distribution has two potential drawbacks: (1) it can be negative, and (2) it isn’t symmetric. Choose some continuous random numeric outcomes of interest to you. Are either potential drawbacks really drawbacks for your random outcomes? If so, which is the more serious drawbacks and why?
(b) Many basketball players and fans believe strongly in the “hot hand.” That is, they believe that players tend to shoot in streaks, either makes or misses. If this is the case, why does the binomial distribution not apply, at least not exactly, to the number of makes in a given number of shots? Which assumption of the binomial model is violated, the independence of successive shots, or the constant probability of success on each shot? Or can you tell? Explain your reasoning.
(c) Your company needs to make an important decision that involves large monetary consequences. You have listed all of the possible outcomes and the monetary payoffs and costs from all outcomes and all potential decisions. You want to use the EMV criterion, but you realize that this requires probabilities and you see no way to find the required probabilities. What can you do?
(d) If your company makes a particular decision in the face of uncertainty, you estimate that it will either gain $10,000, gain $1000, or lose $5000, with probabilities 0.40, 0.30, and 0.30, respectively. You (correctly) calculate the EMV as $2800. However, you distrust the use of this EMV for decision-making purposes. After all, you reason that you will never receive $2800, you will receive $10,000, $1000, or lose $5000. Discuss this reasoning.
(e) In the previous question, suppose you have the option of receiving a check for $2700 instead of making the risky decision described. Would you make the risky decision, where you could lose $5000, or would you take the sure $2700? What would influence your decision?
(f) A potentially huge hurricane is forming in the Caribbean, and there is some chance that it might make a direct hit on Hilton Head Island, South Carolina, where you are in charge of emergency preparedness. You have made plans for evacuating everyone from the island, but duh n evacuation is obviously costly and upsetting for all involved, so the decision to evacuate shouldn’t be made lightly. Discuss how you make such a decision. Is EMV a relevant concept in this situation? How would you evaluate the consequences of uncertain outcomes?
(g) You often hear about the trade-off between risk and reward. Is this trade-off part of the decision making under uncertainty when the decision-maker uses the EMV criterion? For example, how does this work in investment decisions?
(h) Under what conditions would you prefer a simple exponential smoothing model to the moving averages method for forecasting a time series? Explain your reasoning!