Answer to Question #171400 in Statistics and Probability for UMAR

Question

Suppose an engineer is 95% confident that the probability of rejecting a product is going to be 0.5 ± 0.2.

1. Use this information to construct a beta prior for θ.

Hint. Use normal approximation for the beta distribution. Note that if X ∼ Beta(α,β), then and.

1. Suppose that the engineer observed 4 rejections among 10 products. Find the posterior distribution for θ using the prior you proposed in (a).

Problem 2. Suppose the posterior distribution of θ is given by a mixture normal distribution: θ|data ∼ 0.5 · N(0,1) + 0.5 · N(10,1).

Find the

1. 95% HPD credible interval of θ.
2. 95% equal-tail credible interval of θ

Answer 1

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