Analyze HT vs HH stopping-time probabilities

Q: Analyze HT vs HH stopping-time probabilities

This question evaluates understanding of discrete probability, stopping-time analysis, pattern occurrence in Bernoulli sequences, derivation of PMFs and expectations, and the ability to generalize results to biased coins.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

Coin-Flip Stopping Game: HT vs HH

You repeatedly flip a coin until either the pattern HT appears (Player A wins) or the pattern HH appears (Player B wins), whichever occurs first. These are evaluated on the last two consecutive flips; ties cannot occur because only one ordered pair can appear at a time.

Assume the coin is fair unless otherwise stated.

Compute P(A wins) and P(B wins) exactly for a fair coin.
For m ≥ 2, derive the probability mass function (PMF) of the stopping time by outcome: P(A wins at flip m) and P(B wins at flip m).
Compute the expected stopping time E[T].
Generalize part (1) to a biased coin with P(H) = p (so P(T) = 1 − p = q). Provide closed-form expressions for P(A wins) and P(B wins).
Validate by simulation with at least 10^6 trials and compare empirical PMFs to the theoretical results.

Analyze HT vs HH stopping-time probabilities

Coin-Flip Stopping Game: HT vs HH

Solution

Comments (0)

Analyze HT vs HH stopping-time probabilities

Overview

Coin-Flip Stopping Game: HT vs HH

Solution

Comments (0)