The computational algorithms that depend on repeated random sampling to get the numerical results are known as Monte Carlo experiments.** **Simulation means a fictitious representation of reality. To obtain the statistical properties of some behavior is known as Monte Carlo simulation.

For example, Monte Carlo simulation of the behavior of repeatedly tossing a coin is, drawing *a large number* of pseudo-random uniform variables from the interval [0,1] at one time, or once at many different times, and assigning values less than or equal to 0.50 as heads and greater than 0.50 as tails.

Monte Carlo is used in various fields. In mathematics, it is used in integration, simulation, and optimization, inverse problems, and philosophy.

The methods of Monte Carlo may vary, but widely there is a particular pattern that follows.

**That pattern is:**

- Defining the domain of the possible inputs
- Randomly generating inputs from a probability distribution over the domain
- Performing a deterministic computation of the inputs generated
- Collecting the results

**While experimenting there are two important considerations- **

- If the distribution of the points is not uniform, then the approximation will be poor.
- The approximation depends on the placement of the points. There are many points. The approximation tends to come out poor if only a few points are randomly placed.

There are few characteristics of a high-quality Monte Carlo simulation. These characteristics are given by Shlomo Sawilowsky.

**The characteristics are as follows:**

- The random number generator has certain characteristics. For example, a long period before the sequence repeats.
- The random number generator produces a value. This value passes the tests for randomness.
- To ensure accurate results, there are enough samples.
- The technique used is a proper sampling technique.
- The algorithm used invalid for what is being modeled.
- It helps in stimulating the phenomenon is the question.

Monte Carlo is applied in various fields. A Monte Carlo simulation assignment gives students a broader view of how it is used in different fields.

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