Apply Bayes theorem with conjugate priors

Q: Apply Bayes theorem with conjugate priors

This is a Statistics & Math interview question from Other for Data Scientist roles. View the full question and solution on PracHub.

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Question

A website’s true daily purchase conversion p is unknown. Prior: p ~ Beta(2, 8). Day 1: 10 purchases out of 120 visits; Day 2: 18 purchases out of 150 visits. (a) Derive the posterior after both days. (b) Compute the posterior mean and a 95% equal-tailed credible interval. (c) Compute P(p > 0.12 | data). (d) Compare your Bayesian 95% interval to a frequentist Wald interval and an exact Clopper–Pearson interval; explain differences and when each is appropriate.

Apply Bayes theorem with conjugate priors

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