Poisson Distributions

Poisson Distributions

Assessment

Flashcard

Mathematics

12th Grade

Hard

Created by

Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

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.

2.

FLASHCARD QUESTION

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).

3.

FLASHCARD QUESTION

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.

4.

FLASHCARD QUESTION

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.

5.

FLASHCARD QUESTION

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.

6.

FLASHCARD QUESTION

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.

7.

FLASHCARD QUESTION

Front

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.

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