Compare Normal and Poisson Distributions in Statistics

Q: Compare Normal and Poisson Distributions in Statistics

This question evaluates understanding of probability distributions by comparing Normal and Poisson in terms of support, parameters, shape, and the derivation of their means and variances, as well as assessing when a discrete count distribution can be approximated by a continuous one.

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Question

Modeling Counts vs. Continuous Measurements

Scenario

You are modeling event counts (e.g., number of clicks) versus continuous measurements (e.g., response time). You need to choose an appropriate distribution and understand when one can approximate the other.

Question

Explain the main differences between the Normal and Poisson distributions (support, parameters, shape, typical use cases).
Under what conditions can a Poisson distribution be approximated by a Normal distribution? State rules of thumb and any corrections.
Derive the mean and variance for each distribution.

Hints: support, parameters, shape, CLT conditions, λ → ∞ approximation.

Compare Normal and Poisson Distributions in Statistics

Modeling Counts vs. Continuous Measurements

Scenario

Question

Solution

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