Compare Normal and Poisson Distributions in Statistics
Company: Apple
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
##### Scenario
You are modeling event counts versus continuous measurements and must choose the appropriate statistical distribution.
##### Question
Explain the main differences between the Normal and Poisson distributions. Under what conditions can a Poisson distribution be approximated by a Normal distribution? Derive the mean and variance for each.
##### Hints
Focus on support, parameters, shape, CLT conditions, λ→∞ approximation.
Quick Answer: 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.