Solve coin probability and Bayesian inference problems
Five RingsData Scientist · Online AssessmentLast updated
This question evaluates probabilistic reasoning, stochastic-process intuition (pattern waiting times and runs), expected-value calculations, and Bayesian parameter estimation competency.
Answer the following coin-related statistics questions:
- You repeatedly toss a fair coin. What is the probability that the pattern HHH appears before the pattern THH?
- You toss a fair coin 15 times. What is the expected length of the longest consecutive run of heads?
- Let θ be the probability of heads for a coin with prior density p(θ) ∝ θ^3 for θ ∈ [0, 1]. After observing 4 tosses, all of which are heads, what is the posterior distribution of θ?
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