1. The Monte Carlo method is a typical:
- A. Analytical solution method
- B. Statistical experiment (sampling) method
- C. Physical measurement method
- D. Inductive-deductive method
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Monte Carlo Simulation - Lesson Exercise
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The Monte Carlo method is a typical:
Monte Carlo Simulation - Lesson Exercise - Quiz Questions
Test your understanding of random sampling, the law of large numbers, and the application of Monte Carlo methods in mathematical calculations.
2. In the geometric probability model for estimating $\pi$, the true theoretical ratio of the square area to the circle area is:
- A. $1 : 1$
- B. $4 : \pi$
- C. $2 : 1$
- D. $3.14 : 1$
3. [Calculation] In a simulation, if a total of $1000$ points were thrown and $785$ of them fell inside the circle, the estimated value of $\pi$ is approximately:
- A. $0.785$
- B. $3.14$
- C. $4.00$
- D. $3.14159$
4. The 'Convergence Curve' shown in the figure below fluctuates wildly in the early stages of the experiment. This indicates that:
- A. There is a bug in the code
- B. The random number generator is unstable
- C. When the sample size is too small, accidental error dominates
- D. The result is wrong
5. According to statistical laws, if you want to increase the accuracy of a Monte Carlo estimation by $10$ times, the number of points thrown usually needs to be increased by:
- A. $10$ times
- B. $20$ times
- C. $100$ times
- D. $1000$ times
6. True or False: Monte Carlo simulation must be run on a computer; humans cannot complete the experiment manually.
- True
- False
7. In which of the following situations is it most suitable to use Monte Carlo simulation instead of ordinary formula calculation?
- A. Calculating the result of $1 + 1$
- B. Solving an extremely complex insurance adjustment model with thousands of random variables
- C. Measuring the area of a regular square
- D. Finding distance based on speed and time
8. When simulating the area under $y = x^2$, the logic for determining a point as a 'hit' should be:
- A. Point coordinates $(x, y)$ satisfy $y \leq x^2$
- B. Point coordinates $(x, y)$ satisfy $y > x^2$
- C. As long as the point falls within the rectangle, it counts as a hit
- D. See if the color of the point is nice
9. The name 'Monte Carlo' comes from:
- A. The name of the inventor's hometown
- B. A famous casino in the Mediterranean, symbolizing its random characteristics
- C. A famous chocolate brand
- D. The supercomputer model required for the method
10. True or False: As long as the sampling point distribution is 'random' enough, the result of Monte Carlo will definitely be credible.
- True
- False