Monte Carlo Analysis Homework Help

Monte Carlo Analysis

Monte Carlo Simulation, also known as probability simulation, is mathematical computational algorithm used to assess and model the probability of different outcomes which is hard to predict because of intervening random variables. This technique is used in risk analysis, decision making and forecasting and can be applied to different fields such as finance, project management, science, manufacturing, engineering, insurance, supply chain, transportation, etc. It performs risk analysis and decision making by creating a model of probability distribution, with all the possible outcomes of factor that has inherent uncertainty.

Monte Carlo Simulation Provides Advantages in Six Sigma .

1. Probabilistic Results. Results show what could occur, yet how likely every result is.

2. Graphical Results. On account of the information a Monte Carlo reproduction produces, it's anything but difficult to make charts of various results and their odds of event. This is significant for conveying discoveries to different partners.

3. Sensitivity Analysis. With only a couple of cases, deterministic examination makes it hard to see which factors sway the result the most. In Monte Carlo recreation, it's anything but difficult to see which data sources had the greatest impact on main concern results.

4. Scenario Analysis. In deterministic models, it's hard to demonstrate various blends of qualities for various contributions to see the impacts of genuinely various situations. Utilizing Monte Carlo reproduction, experts can see precisely which information sources had which esteems together when certain results happened. This is significant for seeking after further investigation.

5. Correlation of Inputs. In Monte Carlo reproduction, it's conceivable to show reliant connections between information factors. It's significant for precision to speak to how, in all actuality, when a few elements goes up, others go up or down in like manner.

Examples - Monte Carlo Simulation

1.) In this problem, you will use Excel (or Matlab or whatever) to generate continuous uniform (0,1) random variables.

a.(5 pts) Generate a single column of 10,000 U(0,1) random variables. Construct the graphical histogram of these results, which should confirm that the distribution is uniform (0,1).

b.(5 pts) Generate two columns of 10,000 U(0,1) random variables, and in a third column, compute the sum of the first two columns. Draw the histogram of this third column and describe the resulting distribution.

c.(5 pts) Repeat b) for 4 columns of U(0,1) random variables.

we shall use the open source statistical package R to answer this question , the complete R snippet is as follows

c<- runif(10000,0,1)

hist(c,col="purple")

#b)
set.seed(1)
a <- runif(10000,0,1)
b<- runif(10000,0,1)

c <- a+b
hist(c,col="yellow")

c# for 4 colums

c<- runif(10000,0,1)

d<- a+b+c
hist(d,col="orange")

The results are