# Random Numbers

Excel has a __RAND__ function and a __RANDBETWEEN__ function.

These functions will only return numbers within a particular range

For more advanced random numbers you can use the Random Number Generation dialog box.

This gives you much greater control

number of variables - the number of columns

number of random numbers - how many values to return per column

random seed/selection - using this number in another session will return the same random number

### Types of Distribution

Uniform | High and Low values. Characterized by lower and upper bounds. Variables are drawn with equal probability from all values in the range. A common application uses a uniform distribution in the range 0...1. |

Normal | Mean and standard deviation. Characterized by a mean and a standard deviation. A common application uses a mean of 0 and a standard deviation of 1 for the standard normal distribution. |

Bernoulli | P value. Characterized by a probability of success (p value) on a given trial. Bernoulli random variables have the value 0 or 1. For example, you can draw a uniform random variable in the range 0...1. If the variable is less than or equal to the probability of success, the Bernoulli random variable is assigned the value 1; otherwise, it is assigned the value 0. |

Binomial | P value and number of trials. Characterized by a probability of success (p value) for a number of trials. For example, you can generate number-of-trials Bernoulli random variables, the sum of which is a binomial random variable. |

Poisson | Lambda Characterized by a value lambda, equal to 1/mean. Poisson distribution is often used to characterize the number of events that occur per unit of time for example, the average rate at which cars arrive at a toll plaza. |

Patterned | Low, High, Step, No of repeats Characterized by a lower and upper bound, a step, repetition rate for values, and repetition rate for the sequence. |

Discrete | Value and probability Characterized by a value and the associated probability range. The range must contain two columns: The left column contains values, and the right column contains probabilities associated with the value in that row. The sum of the probabilities must be 1. |

### Using Random Number Generation

**Number of Variables** - Enter the number of columns of values you want in the output table. If you do not enter a number, Microsoft Excel fills all columns in the output range you specify.**Number of Random Numbers** - Enter the number of data points you want to see. Each data point appears in a row of the output table. If you do not enter a number, Excel fills all rows in the output range you specify.**Distribution** - Click the distribution method you want to use to create random values.**Parameters** - Enter values to characterize the distribution selected.**Random Seed** - Enter an optional value from which to generate random numbers. You can reuse this value later to produce the same random numbers.**Output Range** - Enter the reference for the upper-left cell of the output table. Excel automatically determines the size of the output area and displays a message if the output table will replace existing data.**New Worksheet Ply** - Click to insert a new worksheet in the current workbook and paste the results starting at cell A1 of the new worksheet. To name the new worksheet, type a name in the box.**New Workbook** - Click to create a new workbook and paste the results on a new worksheet in the new workbook.

The Random Number Generation analysis tool fills a range with independent random numbers drawn from one of several distributions. You can characterise subjects in a population with a probability distribution.

For example, you might use a normal distribution to characterize the population of individuals' heights, or you might use a Bernoulli distribution of two possible outcomes to characterize the population of coin-flip results.

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