LectureNote 05 Flashcards
What is Monte Carlo Simulation?
A probabilistic method used to model and analyze systems influenced by randomness or uncertainty.
What are the key components of Monte Carlo Simulation?
- Random Variables
- Model
- Random Sampling
- Output Analysis
Fill in the blank: Monte Carlo Simulation involves generating a large number of _______ for a model.
random inputs
What is the first step in the Monte Carlo Simulation process?
Define the Problem
Which probability distributions are commonly used in Monte Carlo Simulation?
- Normal distribution
- Uniform distribution
- Exponential distribution
What is the purpose of generating random samples in Monte Carlo Simulation?
To draw random samples from the probability distribution of each input variable.
How are results analyzed after running Monte Carlo simulations?
By extracting statistical properties of the system’s behavior, such as mean and variance.
True or False: Monte Carlo Simulation can only be used in finance.
False
What application of Monte Carlo Simulation is used for option pricing models?
Finance
What does the Monte Carlo approach in engineering involve?
Modeling the failure rate of different components using probability distributions.
In the context of Monte Carlo Simulation, what does ‘Output Analysis’ refer to?
Analyzing the results to assess the system’s performance based on simulation outcomes.
What is a significant advantage of Monte Carlo Simulation?
Flexibility in modeling complex systems with uncertain behavior.
What is a disadvantage of Monte Carlo Simulation?
Computational Expense
Fill in the blank: The accuracy of Monte Carlo Simulation results depends on the number of _______.
iterations
What is the role of a Random Number Generator in Monte Carlo Simulation?
To generate random numbers for sampling from probability distributions.
What is a potential problem with the random number generation technique in Monte Carlo Simulation?
It can lead to biased or misleading results if poorly chosen.
What kind of problems can Monte Carlo Simulation be applied to?
- Stochastic processes
- Deterministic problems
What is one application of Monte Carlo Simulation in medicine?
Estimating the success rate of a new drug.
What is the outcome of using Monte Carlo Simulation in traffic flow and urban planning?
Optimizing signal timings and improving traffic flow.
Fill in the blank: Monte Carlo Simulation can be used to estimate project completion times under _______.
uncertainty
What does sensitivity to assumptions mean in the context of Monte Carlo Simulation?
Results depend heavily on the assumed distributions and parameters for uncertain variables.
What is the first known application of Monte Carlo Simulation?
Used by scientists working on the atom bomb in 1940.
What can generate one or many random numbers?
Random number generators
Random number generators can be hardware-based (true random generators) or pseudo-random number generators.
What is random number generation?
A process that generates a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance
Often involves a random number generator (RNG).
What do Monte Carlo simulations rely on?
Random number generators (RNGs)
They produce pseudo-random numbers that represent the variability of the system being modeled.
How are pseudo-random numbers generated?
Using algorithms to mimic the behavior of true random numbers
Examples include linear congruential generators and the Mersenne Twister.
What is a common approach in Monte Carlo simulations?
To generate uniformly distributed numbers between 0 and 1, then transform them to fit the desired probability distribution
This helps in accurately modeling various scenarios.
What is the seed in random number generation?
An initial value needed by the random number generator
Different seeds yield different sequences of ‘random’ numbers.
True or False: The same seed in random number generation will yield different sequences of numbers.
False
The same seed will give the same sequence for reproducibility.
Fill in the blank: Random number generation is a process that generates a sequence of numbers or symbols that cannot be reasonably predicted better than by _______.
random chance
What is an example of a true random number generator?
Hardware-based random number generators
These generate true randomness, unlike pseudo-random generators.
