Poisson Distributions

Front

What is a Poisson Distribution?

Back

A Poisson Distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given that these events occur with a known constant mean rate and independently of the time since the last event.

Front

What is the formula for calculating the probability of observing k events in a Poisson Distribution?

Back

P(X=k) = (λ^k * e^(-λ)) / k! where λ is the average number of events in the interval, k is the number of events, and e is Euler's number (approximately 2.71828).

Front

If a part has a defect probability of 0.02 and 300 parts are produced, what is the average number of defective parts?

Back

λ = 300 * 0.02 = 6 defective parts.

Front

What is the probability of finding exactly 5 defective parts when the average is 6?

Back

Using the Poisson formula: P(X=5) = (6^5 * e^(-6)) / 5! = 0.1606.

Front

How do you interpret the parameter λ in a Poisson Distribution?

Back

λ represents the average rate of occurrence of the event in the given interval.

Front

What is the probability of producing exactly 3 defective parts if the average is 2?

Back

Using the Poisson formula: P(X=3) = (2^3 * e^(-2)) / 3! = 0.1804.

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What is the significance of the Poisson Distribution in real-world applications?

Back

It is used to model the number of times an event occurs in a fixed interval, such as the number of phone calls received at a call center in an hour.

Front

If a rare event occurs on average 3 times per hour, what is the probability of it occurring 5 times in the next hour?

Back

Using the Poisson formula: P(X=5) = (3^5 * e^(-3)) / 5! = 0.1008.

Front

What does it mean if a Poisson Distribution is used to model an event?

Back

It means that the events are independent, and the average rate of occurrence is constant over the interval.

Front

What is the relationship between the Poisson Distribution and the Exponential Distribution?

Back

The time between events in a Poisson process follows an Exponential Distribution.