How to use EXPONDIST function in Excel?

The `EXPONDIST` function in Excel is used to calculate the exponential distribution, which is typically used to model the time between events in a Poisson process. This can be useful, for example, in determining the time until a given event occurs, such as the time between arrivals of buses or the lifetime of electronic components.

Syntax

EXPONDIST(x, lambda, cumulative)

x: The value of the random variable. It must be non-negative.
lambda: The parameter of the distribution, denoting the rate at which events occur. It must be a positive number.
cumulative: A logical value that determines the form of the function. If TRUE, `EXPONDIST` returns the cumulative distribution function; if FALSE, it returns the probability density function.

Usage

Cumulative Distribution Function (CDF):

If you set `cumulative` to TRUE, `EXPONDIST` will return the probability that the random variable X is less than or equal to x. This is useful for finding probabilities up to a certain value.
Formula Example: `=EXPONDIST(1, 0.5, TRUE)`

Probability Density Function (PDF):

If you set `cumulative` to FALSE, `EXPONDIST` will return the value of the probability density function at x. This is useful for finding probabilities at a specific value.
Formula Example: `=EXPONDIST(1, 0.5, FALSE)`

Example

Let’s say we want to calculate both the cumulative probability and the probability density for an event occurring at exactly 1 unit of time, with a rate parameter of 0.5.

Cumulative Probability (Time ≤ 1):

Formula: `=EXPONDIST(1, 0.5, TRUE)`
This will yield a result that represents the cumulative probability that the event will occur at or before 1 unit of time.

Probability Density (Time = 1):

Formula: `=EXPONDIST(1, 0.5, FALSE)`
This will yield the probability density at exactly 1 unit of time.

Keep in mind that as of Excel 2010, the `EXPONDIST` function has been replaced by the `EXPON.DIST` function, which works in the same way but offers improved accuracy and is consistent with other statistical functions that have been updated. If you’re using a version of Excel from 2010 onwards, it is recommended to use `EXPON.DIST` instead.

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