Monte Carlo simulations - estimating area by throwing darts
1. (x, y) what are the coordinates of a randomly generated point? 2. Where is the randomly generated point located? Inside or outside the region of interest? 3. How many points were generated? 4. What proportion of the points where within each area of interest? 5. What is the known area? 6. What is the equation? 7. What are the known parts of the equation for this particular problem? What is the unknown we are trying to find? Is some algebra needed or can the equation be used as is?
Netlogo TURTLES randomly scatter, then turn into either a COW or a HOUSE depending on whether they hit the BULLS EYE or missed the oval shaped bulls eye.
Know and understand the formula for coming up with a Monte Carlo estimated area when you know the proportion of or the actual count of "darts" that landed inside the area of interest.
Example: Look at the following diagram which shows a solid point for every dart that was thrown and where it hit inside the target area. The target area is the rectangle there you see that goes from x = 1 to x = 3 and from y = 4 to y = 8. (Note: for practical purposes, only 16 or 20 darts were thrown in the examples shown here). Calculate what the estimated area of the region above function g and below function h would be? (The area BETWEEN function g and function h). Please show your work and calculations. I need to see your process of arriving at the result. You will get partial credit if your equation is correct, but you just had a simple calculation, arithmetic error. You will NOT get full credit for just having the correct answer, so show the process for that reason too.