Goldman Sachs·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Goldman Sachs SWE interview had at least one probability question that felt more like a math exam than anything coding-related. Not what I was expecting going in.

Questions Asked (1)

Given a random variable X with PDF f(x) = 0.5 * e^(-|x|) for all real x, compute P(2 ≤ |X| ≤ 4) rounded to three decimal places. Options: A. 0.117, B. 0.018, C. 0.135, D. 0.068.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I stared at this longer than I'd like to admit.

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AI HintsAI Generated

Suggested Approach

Recognize that the PDF is symmetric about 0, so P(2 ≤ |X| ≤ 4) = 2 * P(2 ≤ X ≤ 4). Compute the integral of the PDF from 2 to 4 and double it, then round to three decimal places.

Pro tip: In interviews, always state the symmetry property first to simplify the calculation, and show the integral steps clearly to demonstrate rigor. Double-check the arithmetic to avoid rounding errors.

1. Identify symmetry

Note that f(x) = 0.5 * e^(-|x|) is an even function, so the probability over symmetric intervals can be simplified.

2. Set up the integral

Express P(2 ≤ |X| ≤ 4) as 2 * ∫_{2}^{4} 0.5 * e^{-x} dx, since for x > 0, |x| = x.

3. Evaluate the integral

Compute ∫_{2}^{4} 0.5 * e^{-x} dx = 0.5 * (e^{-2} - e^{-4}). Multiply by 2 to get e^{-2} - e^{-4}.

4. Calculate numerical value

Compute e^{-2} ≈ 0.135335 and e^{-4} ≈ 0.018316, then subtract to get ≈ 0.117019.

5. Round and match

Round to three decimal places: 0.117. Compare with options; the correct choice is A.

Key Points to Mention

Symmetry of the PDF about 0
Definition of absolute value in the interval
Integration of exponential function
Numerical approximation of e^{-2} and e^{-4}
Rounding to three decimal places
Matching the result to the given options

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.