A forest consists of 1,000 trees forming a perfect 50Ã20 rectangle. The northwestern (top-left) corner tree catches fire. Wind blows from the west, therefore, the probability that any tree catches fire from its burning left neighbor is 0.8. The probabilities to catch fire from trees immediately to the right, above, or below are all equal 0.3. 1. Conduct a Monte Carlo study to estimate the probability that more than 30% of the forest will eventually be burning. With probability 0.95, your answer should differ from the true value by no more than 0.005.
2. Based on the same study, predict the total number of affected trees X.
3. Estimate Std(X) and comment on the accuracy of your estimator of X.
4. What is the probability that the actual number of affected trees differs from your estimator by more than 25 trees?
5. A wooden house is located in the northeastern corner of the forest. Would you advise the owner that her house is in real danger?