Poisson distribution, in statistics, a distribution function useful for characterizing events with very low probabilities. In this example, u = average number of occurrences of event = 10. Usage of the Poisson distribution equation can be visibly seen for improving productivity and operating efficiency of a firm. Here we discuss how to calculate the Probability of X using the Poisson distribution formula in excel with examples and a downloadable excel template. Hence there is very little probability that the company will have to 10 claims per day, and it can make its premium based on this data. P(x<=15) = POISSON.DIST(15,10, TRUE) = 95.1%. Therefore, the calculation of the Poisson distribution can be done as follows. French mathematician Simeon-Denis Poisson developed this function to describe the number of times a gambler would win a rarely won game of chance in a large number of tries. So, to evaluate its premium amount, the insurance company will determine the average number of a claimed amount per year. A number of maximum and minimum and clicks on a website. In this example, u = average number of occurrences of event = 10 And x = 15 Therefore, the calculation can be done as follows, P (15;10) = e^(-10)*10^15/15! Mean and Variance of Poisson distribution: If \(\mu\) is the average number of successes occurring in a given time interval or region in the Poisson distribution. Hence P(15;10) = POISSON.DIST (15,10,FALSE) =0.0347 =3.47%. Average sales would be $10,200 at that time. Poisson Distribution Expected Value. Cumulative= its value will be False if we need the exact occurrence of an event and True if a number of random events will be between 0 and that event. Factorial of a number is a product of that integer and all integer below. We will take the same example 1 that we have taken above. In the same way, there is a 50.3% probability for $10,200 or lesser dell on a day. For a Poisson Distribution, the mean and the variance are equal. Let us take a simple example of a Poisson distribution formula. x= number of occurrences for which probability needs to be known, Mean = average number of occurrences during the time period. The Poisson distribution equation is very useful in finding out a number of events with a given time frame and known rate. Then the mean and the variance of the Poisson distribution are both equal to \(\mu\). Now we will find out the probability of $10,000 or lower sales on a day so that breakeven can be achieved, P(10,000,10200) = POISSON.DIST(10200,10000,TRUE). To find out visitors’ footfalls in a mall, restaurant, etc. value of e is 2.72, x! Let’s say the average number of claims handled by an insurance company per day is 5. 4! Based on the maximum number of the claim amount and the cost and profit from the premium, the insurance firm will determine what kind if premium amount will be good to break even its business. To find out the maximum and a minimum number of sales in odd hours and find out whether it is viable to open a store at that time. To find out the probability of the maximum number of patients arriving at a time frame. That means the probability of occurrence of the event between 0 and 15 with 15 inclusive is 95.1%. For Example, let’s say the average cost of operating on a day is $10,000 from 12 am to 8 pm. In the call center industry, to find out the probability of calls, which will take more than usual time and based on that finding out the average waiting time for customers. It means that E(X) = V(X) Where, V(X) is the variance. A random variable is said to have a Poisson distribution with the parameter λ, where “λ” is considered as an expected value of the Poisson distribution. Here we got the exact value using basic excel formula. This has been a guide to Poisson Distribution. = It is known as x factorial. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo.