Compute averages and binomial/Poisson probabilities

Q: Compute averages and binomial/Poisson probabilities

This question evaluates proficiency in streaming summary-statistics updates and probability calculations, specifically computing an updated mean from aggregated summaries and comparing Binomial versus Poisson probability computations within the Statistics & Math domain.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

Streaming Mean and Binomial vs Poisson Approximation

Part A — Streaming Mean Update

You have an existing dataset of N = 1,000 observations with mean 12.4. You:

Remove r = 50 observations whose mean is 20.1, then
Append a = 30 new observations whose mean is 9.8.

Without recomputing from raw data, compute the exact new mean. Show the formula you use and report the final value to 3 decimal places.

Part B — Binomial vs Poisson Approximation

Let X ~ Binomial(n = 40, p = 0.07).

Compute P(X = 0), P(X ≤ 2), and P(X ≥ 3) exactly. Report each to 4 decimal places.
Approximate the same three quantities using a Poisson(λ = n·p) model (use continuity only if appropriate), and report absolute errors for each quantity (|exact − approx|).
Briefly justify when the Poisson approximation is appropriate here, and how you would tighten the approximation if p were larger.

Compute averages and binomial/Poisson probabilities

Streaming Mean and Binomial vs Poisson Approximation

Part A — Streaming Mean Update

Part B — Binomial vs Poisson Approximation

Solution

Comments (0)

Compute averages and binomial/Poisson probabilities

Overview

Streaming Mean and Binomial vs Poisson Approximation

Part A — Streaming Mean Update

Part B — Binomial vs Poisson Approximation

Solution

Comments (0)