Geometric and Poisson Distributions

Front

What is a Geometric Distribution?

Back

A probability distribution that models the number of trials needed for the first success in a series of independent Bernoulli trials.

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What is a Poisson Distribution?

Back

A probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space, given a known average rate of occurrence.

Front

What is the formula for the probability mass function of a Geometric Distribution?

Back

P(X = k) = (1-p)^(k-1) * p, where p is the probability of success.

Front

What is the formula for the probability mass function of a Poisson Distribution?

Back

P(X = k) = (λ^k * e^(-λ)) / k!, where λ is the average rate of occurrence.

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How do you calculate the expected value of a Geometric Distribution?

Back

E(X) = 1/p, where p is the probability of success.

Front

How do you calculate the expected value of a Poisson Distribution?

Back

E(X) = λ, where λ is the average rate of occurrence.

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What is the variance of a Geometric Distribution?

Back

Var(X) = (1-p) / p^2.

Front

What is the variance of a Poisson Distribution?

Back

Var(X) = λ.

Front

If the average number of events is 5, what is the probability of observing exactly 3 events in a Poisson Distribution?

Back

P(X = 3) = (5^3 * e^(-5)) / 3! = 0.1404.

Front

What is the relationship between the Poisson and Exponential distributions?

Back

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