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Excel

POISSON.DIST is a function in Excel that calculates the probability of a given number of events occurring in a given time period, using the Poisson distribution. To use POISSON.DIST, you need to know the number of events that occurred, the average number of events that occurred per unit of time, and the time period. You can then use the POISSON.DIST function to calculate the probability of the number of events occurring.

The syntax of POISSON.DIST in Excel is as follows:

=POISSON.DIST(x, mean, cumulative)

x is the number of events you are expecting mean is the average number of events you are expecting cumulative is a logical value that specifies the cumulative distribution. If cumulative is TRUE, the function returns the cumulative distribution. If cumulative is FALSE, the function returns the probability density function.

POISSON.DIST is used to calculate the probability of a specific number of events occurring in a given time frame. In Excel, this function is used by entering the number of events you expect to occur, the time frame you are measuring in seconds, and the desired probability. An example of how to use POISSON.DIST in Excel can be found below.

In this example, we are calculating the probability of 3 events occurring in a 10-second time frame. First, we enter the number of events we expect to occur (3) into cell A2. Next, we enter the time frame we are measuring in seconds (10) into cell B2. Finally, we enter the desired probability (0.1) into cell C2. By pressing the "enter" key, Excel will calculate the probability of 3 events occurring in 10 seconds. As shown in the table below, the probability is 0.0029.

POISSON.DIST should not be used when the input data is not evenly distributed. For example, if you are trying to calculate the probability of getting a certain number of heads when flipping a coin, the input data is not evenly distributed because the probability of getting a head is not always the same.

There are a few similar formulae to POISSON.DIST in Excel. The first is POISSON.INV, which is the inverse of POISSON.DIST. This formula can be used to find the probability of a specific number of events occurring in a given interval, given a known lambda. The second is POISSON.DIST.R, which is a revised version of POISSON.DIST that is more accurate for small samples. This formula is useful for finding the probability of a specific event occurring in a given interval, given a known lambda. Finally, the NORM.P.DISTRIBUTION function can be used to find the probability of a specific event occurring in a given interval, given a known mean and standard deviation.

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