Calculate Expected Streaks in Coin Toss Sequence

Q: Calculate Expected Streaks in Coin Toss Sequence

This question evaluates understanding of probability theory and expected-value reasoning in discrete stochastic processes, specifically reasoning about runs or streak counts in repeated Bernoulli trials.

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Question

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

For 1,000 tosses of a fair coin, compute the expected number of streaks.
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.

Calculate Expected Streaks in Coin Toss Sequence

Expected Number of Streaks in Coin Tosses

Scenario

Task

Hints

Solution

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