# Documentation/Calc Functions/PROB

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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.

di are all the values in Data

pi are all the values in Probability

Start is Start

End is End

statisfying Start<= di <= 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

None

PROB