Quant Interview Question #quant

quantprof · Intermediate ·🔢 Mathematical Foundations ·2mo ago

Key Takeaways

Solving a quant interview question involving independent normal random variables with mean zero and variance one, specifically calculating the probability that the sum of the squares of two variables exceeds the square of a third variable.

Full Transcript

Let N1, N2, and N3 be independent normal random variables with mean zero and variance one. What is the probability that N1 squared plus N2 squared is greater than N3 squared? Post your answers in comments.

Original Description

Can you solve this quant interview question?
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This video teaches how to solve a quant interview question involving independent normal random variables, calculating the probability of a specific event. The question requires applying statistical concepts and mathematical modeling to derive the solution. Viewers will learn how to approach similar problems and calculate probabilities in statistical analysis.

Key Takeaways
  1. Define the problem and identify the key elements: independent normal random variables with mean zero and variance one.
  2. Calculate the probability that N1 squared plus N2 squared is greater than N3 squared using statistical concepts and mathematical modeling.
  3. Apply the concept of independent variables and calculate the joint probability distribution.
  4. Use the properties of normal random variables to simplify the calculation and derive the final probability.
  5. Post the answer in the comments and discuss the solution with others.
💡 The key insight in this problem is recognizing that the sum of the squares of two independent normal random variables follows a chi-squared distribution, which can be used to calculate the desired probability.

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