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This is a medium difficulty Machine Learning question, commonly asked during Onsite rounds at J.P. Morgan.

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This question is commonly asked for Data Scientist candidates at J.P. Morgan during technical interviews.

Test whether samples follow a binomial distribution

Last updated: Mar 29, 2026

Quick Overview

This question evaluates a candidate's understanding of statistical hypothesis testing, goodness-of-fit assessment for discrete distributions, parameter estimation for parametric models, and interpretation of inferential results.

J.P. Morgan

Jan 22, 2026, 12:00 AM

Data Scientist

Onsite

Machine Learning

You collect a dataset that you believe comes from a binomial process. Each observation is a count of successes.

You have i.i.d. samples $x_1,\dots,x_m$ , where each $x_i$ is the number of successes out of $n$ trials.
You want to test whether the sample distribution is consistent with $\text{Binomial}(n, p)$ for some (possibly unknown) $p$ .

Question: What statistical test(s) would you use to assess whether the sample distribution follows a binomial distribution, and how would you perform the test (hypotheses, parameter estimation, test statistic, assumptions, and interpretation)?

Solution

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