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Point72 Asset Management·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Apr 2026

Summary

Got a probability question for a quant role at Point72. Short and sweet on the surface, but it requires you to actually think about geometry or covariance, not just plug into a formula.

Questions Asked (1)

Q1

X and Y are independent standard normal random variables. What is P[X > 3Y]?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

My first instinct was to set up an integral and I immediately started second-guessing myself on the bounds.

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AI HintsAI Generated

Suggested Approach

Recognize that X - 3Y is a linear combination of independent normals, hence normally distributed with mean 0 and variance 10. Then compute P[X - 3Y > 0] = 1/2 by symmetry, and explain the reasoning clearly.

Pro tip: Emphasize that the result is exactly 1/2 due to symmetry, not an approximation, and connect it to the fact that any symmetric continuous distribution has equal probability above and below its mean.

1. Define the event

Rewrite the inequality as X - 3Y > 0 to simplify the comparison.

2. Identify distribution

Since X and Y are independent normal, X - 3Y is also normal. Compute its mean and variance: mean = 0, variance = 1 + 9 = 10.

3. Use symmetry

A normal distribution is symmetric about its mean, so P[X - 3Y > 0] = P[X - 3Y < 0] = 1/2.

4. Conclude and verify

State the final answer as 1/2, and optionally verify by standardizing or noting that the probability does not depend on the variance.

Key Points to Mention

  • Linear combination of independent normals is normal
  • Mean of X - 3Y is 0
  • Variance of X - 3Y is 1 + 9 = 10
  • Symmetry of the normal distribution about its mean
  • Probability equals 1/2 exactly
  • No need to compute integrals or use tables

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