Compute posterior and predictive coin probabilities

Q: Compute posterior and predictive coin probabilities

This question evaluates Bayesian inference and probabilistic reasoning, focusing on posterior updating, posterior predictive probability, and the conditional expectation of a stopping time given observed outcomes.

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Question

Bayesian coin: posterior, prediction, and stopping-time expectation

Context

You have two coins and will use the same coin for all flips:
- Fair coin F: P(H) = 0.5
- Biased coin B: P(H) = 0.7
You pick one coin uniformly at random (P(F) = P(B) = 0.5).
You flip the chosen coin three times. The first two flips are Heads (H, H). The third flip is not yet observed.

Tasks

(a) Compute P(B | first two flips are Heads).

(b) Compute P(next flip is Heads | first two flips are Heads).

(c) Continuing with the same coin, let T be the total number of flips until the first Tail occurs (including that Tail). Compute E[T | first two flips are Heads], and show your derivation.

Compute posterior and predictive coin probabilities

Bayesian coin: posterior, prediction, and stopping-time expectation

Context

Tasks

Solution

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Compute posterior and predictive coin probabilities

Overview

Bayesian coin: posterior, prediction, and stopping-time expectation

Context

Tasks

Solution

Comments (0)