Poisson Distribution Ira Pre assesment -Lalita

What is the Poisson distribution used for?

• Modeling the number of events occurring in a fixed interval of time or space

• Modeling the weather patterns

• Predicting stock market trends

• Estimating the average height of a population

What are the key characteristics of a Poisson distribution?

• Variable rate

• Continuous

• Predictable

• Discrete, fixed interval, constant rate, memoryless

• Non-parametric

What is the formula for calculating the Poisson probability?

• P(x; λ) = (e^-λ * λ^x) / x^3

• P(x; λ) = (e^-λ * λ^x) / x!

• P(x; λ) = (e^-λ * λ^x) / x

• P(x; λ) = (e^-λ * λ^x) / x^2

In a Poisson distribution, what does lambda represent?

• Total number of occurrences

• Standard deviation of occurrences

• Median rate of occurrence

• Average rate of occurrence

What is the mean and variance of a Poisson distribution?

• Mean = 2λ, Variance = 2λ

• Mean = λ, Variance = λ

• Mean = λ, Variance = 2λ

• Mean = 0, Variance = 0

What is the relationship between the mean and variance in a Poisson distribution?

• Mean is greater than variance

• Mean is less than variance

• Mean is unrelated to variance

• Mean is equal to variance

What are some real-world applications of the Poisson distribution?

• Estimating the number of customers in a store

• Predicting the outcome of a coin flip

• Forecasting stock prices

• Modeling phone calls at a call center, estimating accidents at an intersection, predicting emails received per day, analyzing radioactive decay

How is the Poisson distribution different from the normal distribution?

• The Poisson distribution is symmetric, while the normal distribution is skewed.

• The Poisson distribution is discrete and used for counting events, while the normal distribution is continuous and used for modeling continuous variables.

• The Poisson distribution is used for continuous variables, while the normal distribution is used for counting events.

• The Poisson distribution assumes a fixed mean and variance, while the normal distribution does not.

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CCSS.HSS.ID.A.3

What is the probability mass function of a Poisson distribution?

• P(X=k) = (λ^k * e^(-λ)) / (k-1)!

• P(X=k) = (λ^k * e^(-λ)) / (k+1)!

• P(X=k) = (λ^k * e^(-λ)) / (k^2)!

• P(X=k) = (λ^k * e^(-λ)) / k!

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

How can you determine if a given dataset follows a Poisson distribution?

• Calculate the median instead of the average rate

• Check if the data represents the number of events occurring in a fixed interval of time or space, if the events are independent, if the average rate is constant, and perform a goodness-of-fit test like the Chi-Square test.

• Verify if the events are dependent on each other

• Check if the data represents the number of events occurring in a random interval of time or space