Quant Interview Question #quant

quantprof · Beginner ·📐 ML Fundamentals ·1w ago

Key Takeaways

Solving a quant interview question involving a random walk on an infinite number line with given probabilities of moving right or left, and calculating the probability of returning to the starting position after 30 seconds using concepts from probability theory and stochastic processes.

Full Transcript

Suppose you start at zero on an infinite number line. Every second, if you are at zero, you move one unit to the right with probability 1 by 2 and stay at zero with probability 1 by 2. If you are at any other position, you move one unit to the right with probability 1 by 2 and one unit to the left with probability 1 by 2. What is the probability that you are back at position zero after 30 seconds? 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 a random walk on an infinite number line, and calculates the probability of returning to the starting position after 30 seconds. The problem requires applying concepts from probability theory and stochastic processes, and can be solved using a recurrence relation or Markov chain analysis.

Key Takeaways
  1. Define the problem and identify the key elements: the infinite number line, the probabilities of moving right or left, and the time frame of 30 seconds.
  2. Determine the approach to solve the problem: using a recurrence relation or Markov chain analysis.
  3. Set up the recurrence relation or Markov chain to model the random walk.
  4. Calculate the probability of returning to the starting position after 30 seconds using the chosen approach.
  5. Post the answer in the comments and discuss the solution with others.
💡 The problem can be solved using a recurrence relation or Markov chain analysis, and the key insight is to recognize that the random walk is a stochastic process with given probabilities of moving right or left.

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