Calculate Expected Streaks in Coin Toss Sequence

Quick Overview

Calculate Expected Streaks in Coin Toss Sequence evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Calculate Expected Streaks in Coin Toss Sequence

Company: Upstart

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Onsite

##### Scenario Tech interview round 1 – probability puzzle about streaks ##### Question We toss a fair coin 1,000 times. Each time the outcome differs from the previous toss, a new streak begins (the first toss also starts a streak). What is the expected number of streaks? Generalise the expected streak count when the coin shows heads with probability p. ##### Hints Indicator for change between toss i and i+1; linearity of expectation.

Quick Answer: Calculate Expected Streaks in Coin Toss Sequence evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025, 10:55 AM
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Calculate Expected Streaks in Coin Toss Sequence

Expected Number of Streaks in Coin Tosses

Scenario

You toss a coin repeatedly. A "streak" (a run) begins on the first toss and whenever the current toss differs from the immediately previous toss.

Task

  1. For 1,000 tosses of a fair coin, compute the expected number of streaks.
  2. Generalize the expected number of streaks for a biased coin where the probability of heads is p.

Assumptions: Tosses are independent; a streak starts on the first toss.

Hints

  • Use an indicator for a change between toss i and i+1.
  • Apply linearity of expectation.

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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