EXPONDIST

Calculates values for an exponential distribution.

Syntax:

EXPONDIST(x, λ, mode)

The exponential distribution is a continuous probability distribution, with parameter λ (rate). λ must be greater than zero.

If mode is 0, EXPONDIST calculates the probability density function of the exponential distribution:

$λ e^{- λ x}$

If mode is 1, EXPONDIST calculates the cumulative distribution function of the exponential distribution:

$1 - e^{- λ x}$

Example:

EXPONDIST(0, 1, 0)

returns 1.

EXPONDIST(0, 1, 1)

returns 0.

Application:

The EXPONDIST function is used to calculate the exponential distribution, which models the time between events in a Poisson process. An application of this is analyzing the time between customer arrivals at a coffee shop.

Let's assume the average time between customer arrivals at a coffee shop is 5 minutes. We can use EXPONDIST to find the probability of a customer arriving within a specific time frame.

The EXPONDIST function has the following arguments:

x: The value at which to evaluate the function. This represents the time we are interested in.
lambda: The rate parameter. This is the inverse of the mean time between events. In our case, the mean time is 5 minutes, so lambda is 1/5 or 0.2.
cumulative: A logical value that determines the type of distribution.
- TRUE: Returns the cumulative distribution function, which gives the probability that a customer arrives within the specified time.
- FALSE: Returns the probability density function, which gives the probability of a customer arriving at a specific time.

Example: Probability of a customer arriving within a certain time

Let's use a table to show the probability of a customer arriving within different time intervals, using the cumulative distribution function (cumulative = TRUE).

Rate (lambda): 0.2 (customers per minute)

	Time (x) in minutes	EXPONDIST(x, 0.2, TRUE)	Interpretation
	A	B	C
1	1	0.1813	There is an 18.13% chance that a new customer will arrive within the first minute.
2	5	0.6321	There is a 63.21% chance that a new customer will arrive within the first 5 minutes.
3	10	0.8647	There is an 86.47% chance that a new customer will arrive within the first 10 minutes.
4	15	0.9502	There is a 95.02% chance that a new customer will arrive within the first 15 minutes.
5	20	0.9817	There is a 98.17% chance that a new customer will arrive within the first 20 minutes.