Explain the concept of simulation.
Simulations use chance devices to model random events and estimate probabilities by repeating trials and analyzing the results.
Explain the concept of the Law of Large Numbers.
As the number of trials in a simulation increases, the simulated (empirical) probabilities converge towards the true probability of the event.
Explain how to conduct a simulation.
1. Describe how to use a chance device to imitate one trial. 2. Repeat many trials of the simulation. 3. Analyze the results to answer your question of interest.
Explain the importance of a large number of trials in a simulation.
A large number of trials ensures that the simulated probability gets closer to the true probability, as stated by the Law of Large Numbers.
Explain how simulations can be used to estimate probabilities.
By modeling random events and repeating trials, simulations provide empirical probabilities that approximate the true probabilities.
What are the differences between an outcome and an event?
Outcome: A single result of a random process. | Event: A collection of one or more outcomes.
What are the differences between simulated probability and true probability?
Simulated Probability: Probability obtained through simulation. | True Probability: Theoretical probability based on the underlying model.
What is the definition of a random process?
A process where the results are determined by chance.
What is the definition of an outcome?
The result of a single trial in a random process.
What is the definition of an event?
A collection of one or more outcomes.
What is the definition of probability?
A number between 0 and 1 that describes the likelihood of an event occurring.
What is the Law of Large Numbers (LLN)?
As the number of trials increases, the simulated probabilities get closer to the true probability.
