Estadística y Probabilidad

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Poisson Distribution Calculator.

Calculate P(X = k) for a Poisson process.

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02 / RESPUESTA

Rate (λ)

Events (k)

probability

0,224042

percent

22,404181

expectedEvents

3,000000

variance

3,000000

Results update automatically as you type.

Use Cases

Quality Control and Defect Analysis

Determine the probability of observing a specific number of defects in a product batch, given the historical average defect rate.

Example: If a factory averages 2 defects per 100 units, what is the probability of exactly 3 defects in a batch of 100?

Traffic and Arrival Rate Planning

Estimate the likelihood of a certain number of customers arriving at a service point within a given time period, based on average arrival rate.

Example: If a store averages 5 customers per 10 minutes, what is the probability of exactly 7 customers arriving in the next 10 minutes?

Frequently Asked Questions

What does the Poisson distribution calculate?: It calculates the probability of a given number of events (k) occurring in a fixed interval, given the average rate (λ) of occurrence. The result is the probability mass function P(X = k).
What are the inputs for this calculator?: You need to provide the rate (λ), which is the average number of events per interval, and the number of events (k) you want the probability for. Both must be non-negative numbers.
Can I use this calculator for any type of events?: Yes, as long as the events are independent and occur at a constant average rate. Common examples include website visits per hour, defects per batch, or phone calls per minute.

Tips & Common Mistakes

Tips

Ensure the rate (λ) is for the same time or space interval as the events (k) you are considering. For example, if λ is per hour, k should be the number of events in one hour.
The Poisson distribution assumes events occur independently and at a constant average rate. Verify these assumptions before applying the result.
Use the calculator to explore how the probability changes with different k values for a fixed λ, which can help in understanding the distribution shape.
For large λ (e.g., >20), the Poisson distribution approximates a normal distribution, but this calculator still gives exact probabilities.

Common Mistakes to Avoid

Using a rate (λ) that is not for the same interval as the events (k). For example, using a daily rate but asking for weekly events without adjusting λ.
Entering negative values for λ or k. Both must be non-negative integers for k and a positive real number for λ.
Confusing the probability of exactly k events with the probability of at most k events. This calculator gives the exact probability P(X = k), not cumulative probabilities.

Last updated: August 13, 2026

Use Cases

Quality Control and Defect Analysis

Determine the probability of observing a specific number of defects in a product batch, given the historical average defect rate.

Example: If a factory averages 2 defects per 100 units, what is the probability of exactly 3 defects in a batch of 100?

Traffic and Arrival Rate Planning

Estimate the likelihood of a certain number of customers arriving at a service point within a given time period, based on average arrival rate.

Example: If a store averages 5 customers per 10 minutes, what is the probability of exactly 7 customers arriving in the next 10 minutes?

Frequently Asked Questions

What does the Poisson distribution calculate?

It calculates the probability of a given number of events (k) occurring in a fixed interval, given the average rate (λ) of occurrence. The result is the probability mass function P(X = k).

What are the inputs for this calculator?

You need to provide the rate (λ), which is the average number of events per interval, and the number of events (k) you want the probability for. Both must be non-negative numbers.

Can I use this calculator for any type of events?

Yes, as long as the events are independent and occur at a constant average rate. Common examples include website visits per hour, defects per batch, or phone calls per minute.

Tips & Common Mistakes

Tips

Ensure the rate (λ) is for the same time or space interval as the events (k) you are considering. For example, if λ is per hour, k should be the number of events in one hour.
The Poisson distribution assumes events occur independently and at a constant average rate. Verify these assumptions before applying the result.
Use the calculator to explore how the probability changes with different k values for a fixed λ, which can help in understanding the distribution shape.
For large λ (e.g., >20), the Poisson distribution approximates a normal distribution, but this calculator still gives exact probabilities.

Common Mistakes to Avoid

Using a rate (λ) that is not for the same interval as the events (k). For example, using a daily rate but asking for weekly events without adjusting λ.
Entering negative values for λ or k. Both must be non-negative integers for k and a positive real number for λ.
Confusing the probability of exactly k events with the probability of at most k events. This calculator gives the exact probability P(X = k), not cumulative probabilities.

Use Cases

Quality Control and Defect Analysis

Determine the probability of observing a specific number of defects in a product batch, given the historical average defect rate.

Example: If a factory averages 2 defects per 100 units, what is the probability of exactly 3 defects in a batch of 100?

Traffic and Arrival Rate Planning

Estimate the likelihood of a certain number of customers arriving at a service point within a given time period, based on average arrival rate.

Example: If a store averages 5 customers per 10 minutes, what is the probability of exactly 7 customers arriving in the next 10 minutes?

Frequently Asked Questions

What does the Poisson distribution calculate?

It calculates the probability of a given number of events (k) occurring in a fixed interval, given the average rate (λ) of occurrence. The result is the probability mass function P(X = k).

What are the inputs for this calculator?

You need to provide the rate (λ), which is the average number of events per interval, and the number of events (k) you want the probability for. Both must be non-negative numbers.

Can I use this calculator for any type of events?

Yes, as long as the events are independent and occur at a constant average rate. Common examples include website visits per hour, defects per batch, or phone calls per minute.

Tips & Common Mistakes

Tips

Ensure the rate (λ) is for the same time or space interval as the events (k) you are considering. For example, if λ is per hour, k should be the number of events in one hour.
The Poisson distribution assumes events occur independently and at a constant average rate. Verify these assumptions before applying the result.
Use the calculator to explore how the probability changes with different k values for a fixed λ, which can help in understanding the distribution shape.
For large λ (e.g., >20), the Poisson distribution approximates a normal distribution, but this calculator still gives exact probabilities.

Common Mistakes to Avoid

Using a rate (λ) that is not for the same interval as the events (k). For example, using a daily rate but asking for weekly events without adjusting λ.
Entering negative values for λ or k. Both must be non-negative integers for k and a positive real number for λ.
Confusing the probability of exactly k events with the probability of at most k events. This calculator gives the exact probability P(X = k), not cumulative probabilities.