1. (8 points) Let's say you were selected to participate in a TV game show. One of the games you will be playing is Cash or Nothing; where you are showed three curtains, two of them have nothing behind and one of them has one million dollars in cash. First you must pick one of the three curtains (curtain #1, curtain #2, or curtain #3). Once you have made a curtain selection, the host will open one of the non-selected curtains that has nothing behind it. At that point, the host will offer you the chance to stay with your original curtain choice or change curtains. (Note: that the host only opens a curtain that did not had the prize behind it.) a. (5 points) Using Excel (or the software of your preference) do a Monte Carlo simulation for all the possible scenarios. Note that I am expecting at least 1 million replicates. If Excel is having trouble handling it, feel free to divide the replications in different sheets and then aggregate the results. Hint: use Excel functions AND, RANDBETWEEN, and IF. (Tip: Use different columns to track the door selected, the winning door, what would have happened if you stayed, what if had changed doors.) b. (3 points) Based on the results from part a, state which option is better: stay with your original curtain selection or change. Justify the results from part a. Is this result intuitive (why or why not)? How can the result be explained? 1. (8 points) Let's say you were selected to participate in a TV game show. One of the games you will be playing is Cash or Nothing; where you are showed three curtains, two of them have nothing behind and one of them has one million dollars in cash. First you must pick one of the three curtains (curtain #1, curtain #2, or curtain #3). Once you have made a curtain selection, the host will open one of the non-selected curtains that has nothing behind it. At that point, the host will offer you the chance to stay with your original curtain choice or change curtains. (Note: that the host only opens a curtain that did not had the prize behind it.) a. (5 points) Using Excel (or the software of your preference) do a Monte Carlo simulation for all the possible scenarios. Note that I am expecting at least 1 million replicates. If Excel is having trouble handling it, feel free to divide the replications in different sheets and then aggregate the results. Hint: use Excel functions AND, RANDBETWEEN, and IF. (Tip: Use different columns to track the door selected, the winning door, what would have happened if you stayed, what if had changed doors.) b. (3 points) Based on the results from part a, state which option is better: stay with your original curtain selection or change. Justify the results from part a. Is this result intuitive (why or why not)? How can the result be explained
