# Documentation/Calc Functions/PROB

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## Function name:

PROB

## Category:

Statistical Analysis

## Summary:

Given a specified probability for each possible value of a discrete random variable, calculates the probability of a sample value lying between two limits.

## Syntax:

PROB(**Data**; **Probability**; **Start**[; **End**])

## Returns:

Returns a real number in the range [0, 1] which is the probability that for the specified probability mass function, a sample value will lie within the specified limits.

## Arguments:

**Data** is an array or a reference to a range of cells containing the possible values of the discrete random variable.

**Probability** is an array or a reference to a range of cells containing the corresponding probabilities for each value in **Data**.

**Start** is a real number or a reference to the cell containing that number which is the start value of the interval whose probabilities are to be summed.

**End** is a real number or a reference to the cell containing that number which is the end value of the interval whose probabilities are to be summed. If this parameter is missing, the probability for the **Start** value is calculated based on the principle that the **Data** values are equal to the value of **Start**.

The function returns the same result if **Start** is greater than **End** by interchanging the two values.

- If any of the values in
**Probability**are less than 0 or greater than 1 or they don't sum up to 1 then the function returns an error value. - If
**Data**and**Probability**have different numbers of data points then the function returns an error value.

## Additional details:

- The formula for PROB is:

where I is the indicator function such that I(x,a,b) denotes the indicator function that is 1 if and 0 otherwise.

d_{i} are all the values in **Data**

p_{i} are all the values in **Probability**

Start is **Start**

End is **End**

statisfying Start<= d_{i} <= End

## Examples:

Data | Probability | |
---|---|---|

1 | 195 | 0.02 |

2 | 151 | 0.03 |

3 | 148 | 0.2 |

4 | 189 | 0.05 |

5 | 183 | 0.15 |

6 | 154 | 0.55 |

Formula | Description | Returns |
---|---|---|

=PROB(A1:A6;B1:B6;160;190) | Returns the probability with which a value within the range of A1:A6 is also within the limits between 160 and 190. Every value within the range of A1:A6 has a probability within the range of B1:B6. | 0.2 |

=PROB(A1:A6;B1:B6;160;170) | No value exists in data between 160 and 170 so the function returns 0 | 0 |

=PROB(A1:A6;B1:B6;151) | Returns the probability associated with the value 151. | 0.03 |

=PROB(A1:A6;B1:B6;170) | Returns the probability associated with the value 170 but this value doesn't exist in the data so the function returns 0. | 0 |

## Related LibreOffice functions:

None

## ODF standard:

## Equivalent Excel functions:

PROB