

Geometric and Poisson Distributions
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a Geometric Distribution?
Back
A Geometric Distribution models the number of trials until the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.
2.
FLASHCARD QUESTION
Front
What is the formula for the probability mass function of a Geometric Distribution?
Back
The probability mass function is given by P(X = k) = (1 - p)^(k-1) * p, where p is the probability of success and k is the trial number of the first success.
3.
FLASHCARD QUESTION
Front
What is a Poisson Distribution?
Back
A Poisson Distribution models the number of events occurring in a fixed interval of time or space, given that these events happen with a known constant mean rate and independently of the time since the last event.
4.
FLASHCARD QUESTION
Front
What is the formula for the probability mass function of a Poisson Distribution?
Back
The probability mass function is given by P(X = k) = (λ^k * e^(-λ)) / k!, where λ is the average rate of occurrence and k is the number of occurrences.
5.
FLASHCARD QUESTION
Front
How do you determine the probability of the first success occurring on the k-th trial in a Geometric Distribution?
Back
You use the formula P(X = k) = (1 - p)^(k-1) * p, where p is the probability of success.
6.
FLASHCARD QUESTION
Front
What is the mean of a Geometric Distribution?
Back
The mean of a Geometric Distribution is 1/p, where p is the probability of success.
7.
FLASHCARD QUESTION
Front
What is the variance of a Geometric Distribution?
Back
The variance of a Geometric Distribution is (1 - p) / p^2.
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