Matlab → Basics → Scripts, Functions → Programming → Graphs → Simulations

The behavior of many real-life system or phenomenon, whether biological, economic, physical, or even sociological, are often described in mathematical terms. The mathematical description of a system of phenomenon is called a mathematical model. And, simulation is a computer program which attempts to represent the real world based on that mathematical model. The accuracy of the simulation depends on the precision of the model.

**Plotting Random Numbers**

We know that the Matlab command

`U=randn(10,1)`

generates 10 normally (or Gaussian) distributed random numbers. In the next example, we are going to generate 1000 normally distributed random numbers and will plot them.

`U=randn(500,1);`

plot(U,'o')

The above command plotted the random numbers. Note that another way of writing the above program is

`n=500;`

U=randn(n,1);

plot(U,'o')

In the next example, we will generate 10,000 normally distributed random numbers and will plot then in a histogram.

`n=10000;`

U=randn(n,1);

bars = 30;

hist(U,bars)

**Simulating a Dice**

The `randi`

command is used to return a random integer, and the command `randi(6)`

returns a random integer between 1 and 6, inclusive. Similarly, the command

`>> dice=randi(6,10,1)`

returns a 10×1 matrix (10 rows and 1 column) of random integers between 1 and 6, inclusive.

Now, roll two dices and calculate sum of the numbers return. Simulate the experiment for 1000 times and plot a histogram. Show that the distribution is normal. For this, the Matlab code looks like,

`dice1=randi(6,1000,1);`

dice2=randi(6,1000,1);

dice=dice1+dice2;

bars=11;

hist(dice,bars)

**NOTE:** For the sum of two dices, the total outcomes are 11 (i.e. 2, 3, 4, …, 12). So, the histogram is divided in 11 bins (or bars).