Solve coin probability and Bayesian inference problems

Q: Solve coin probability and Bayesian inference problems

This question evaluates probabilistic reasoning, stochastic-process intuition (pattern waiting times and runs), expected-value calculations, and Bayesian parameter estimation competency.

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Question

Coin-Flip Statistics: Pattern Racing, Runs, and Bayesian Updating

You are given three independent questions about fair coin tossing and Bayesian updating. Assume all flips are independent.

Tasks

Repeatedly toss a fair coin until either pattern HHH or pattern THH appears. What is the probability that HHH appears before THH?
Toss a fair coin 15 times. What is the expected length of the longest consecutive run of heads?
Let θ be the (unknown) probability of heads for a coin with prior density p(θ) ∝ θ^3 on [0, 1]. After observing 4 tosses, all of which are heads, what is the posterior distribution of θ?

Solve coin probability and Bayesian inference problems

Coin-Flip Statistics: Pattern Racing, Runs, and Bayesian Updating

Tasks

Solution

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Solve coin probability and Bayesian inference problems

Overview

Coin-Flip Statistics: Pattern Racing, Runs, and Bayesian Updating

Tasks

Solution

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