Apple·Data Scientist·Technical Phone Screen
- You have 200 independent minute-level event counts with sample mean 14.5 and sample variance 16.2. Under a Poisson model, derive the MLE for lambda, its asymptotic variance, and build a 95% Wald confidence interval.
- Test whether the data follows a Poisson distribution (equidispersion) versus being overdispersed. Specify the test statistic, its reference distribution, and give a decision at alpha=0.05 using the provided sample mean and variance.
- For a single Poisson random variable with lambda=120, approximate P(100 <= X <= 140) using the Normal approximation with continuity correction. Write out the exact Normal integral and explain why the correction matters.
- Under what conditions is a Normal approximation to a Poisson valid, when does it break down, and what alternative model would you use when the sample variance is much larger than the sample mean? Name one diagnostic you'd check.
“MLE derivation was fine, lambda-hat equals x-bar, straightforward log-likelihood stuff.”