# Random Numbers in Modeling and Simulation

### Random Number

Random number that occur in a sequence such that two condition are satisfy-

i) The value are unformaly distributed over a defined interval or set.

ii) It is possible to predicts future values based on past or present one.

It is called random if it satisfy, about to properties or condition:-

1). The interval of above example is head or tail. All the expected result is under the given interval. Therefore it is unformaly distributed over a defined internal.

2). If we toss coins in first time suppose result is Head Tail, then it is difficult to find the result when we toss coins second time. Therefore second property satisfy because we are not able to predict the result using past or present result.

Tossing two coins satisfy both first and second properties or condition of random number. There we call tossing two coins is a random event.

Similarity: Rolling dice is also a random number.

### Numbers are divided into two categories:

#### i). Truly random number:

Truly Random Numbers is the physical method of generating random numbers.

#### ii). Pseudo random numbers:

Pseudo Random Numbers is the computational method of generating random numbers.

Let's discuss about these two types of random numbers briefly:

### ✓Truly Random Numbers

Random Numbers in which there is no correlation of the previous number with its successor is called Truly Random Numbers.

• In Truly Random Number we are not able to predict the next Random Number.

• And we cannot regenerate the random number series with the help of truly random number.

#### Example of Truly Random Numbers

i) Rolling Dices

ii) Tossing Coins

iii) Roulette Wheels, etc.

#### Disadvantages of Truly Random Number:

Truly Random Numbers are slower than Pseudo Random Numbers

This type of random number is non-deterministic number which means we cannot predict the next number with the help if Truly Random Number.

To implement Truly Random Number we required extra hardwares.

And the series of random number generated by truly random number is not reproducible.

### ✓Pseudo Random Numbers

Random numbers in which there is correlation of the previous number with its successor is called Pseudo Random Number.

• Pseudo Random Numbers are look random but its number or depend on the previous number.

• Using the same initial random number we can regenerate the same series of random numbers.

#### Disadvantages of Pseudo Random Numbers:

To overcome all the disadvantage of Truly Random Number should a number is used:

Pseudo Random Number are faster then Truly Random Number. i.e. Long sequence of random numbers can be produced very quickly.

Random Number is deterministic, that means we can predict the next number in pseudo random number series.

The series generated by pseudo random number is reproducible. Means all sequence eventurly repeat themself when same initial condition is used.

To implement Pseudo Random Number we does not required extra hardware.

Pseudo Random Number is closely approximate the ideal properties of random number:

• Uniformity

• Independence