146 Simulating the Stock Market 3.1 ACTIVITY APPLET You can find the interactive applet for this activity at MyLab Statistics. 146 CHAPTER 3 Probability The Simulating the stock market applet allows you to investigate the probability that the stock market will go up on any given day. When the 1 day or 5 days buttons are clicked, the results of the corresponding number of daily outcomes are added to the Days column. For each day, a green arrow indicates the market going up and a red arrow indicates the market going down. Clicking the 1000 days button will add the 1000 daily outcomes as fast as possible by skipping the animation. The cumulative results of the daily outcomes are given in the plot showing the cumulative proportion of up outcomes versus the total number of days. The tallied results are also stored in the table above the graph. The green line in the plot reflects the true probability of the market going up on any given day, which is set to 1/2 = 0.5. In this case, the market has a 50% chance of going up on any given day. As more and more outcomes are simulated, the cumulative proportion of “up” days should converge to this value. Day # 2 0 1 8 6 4 10 0.8 0.6 0.4 0.2 Stock Market 1 day 5 days 1000 days Outcomes Reset Days Event Up Proportion of “Up” Days Convergence Count Total Proportion EXPLORE Step 1 Click 1 day twelve times. Click Outcomes and Convergence. Step 2 Click Reset. Step 3 Click 5 days four times. Click Reset. Step 4 Click 1000 days four times. DRAW CONCLUSIONS 1. Run a simulation by clicking 1 day several times without clicking Reset. How many days did it take until there were three straight days on which the stock market went up? three straight days on which the stock market went down? 2. Run a simulation of the stock market for 35 business days. Find the empirical probability that the market goes up on day 36. APPLET
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