You are going to take a sample of measurements of specific gravity of a chemical product being produced. You know the specific gravity measurements are approximately normal(μ , σ²) where σ² = .005². You have precise normal(1.10, .001²) prior for μ because the manufacturing process is quite stable. However, you have a nagging doubt about whether the process is correctly adjusted, so you decide to use a mixture prior. You let g₀(μ) be your precise normal(1.10, .001²) prior, you let g₁(μ) be a normal(1.10, .01²), and you let p₀ = .95. You take a random sample of product and measure the specific gravity. The measurements are

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501.5 499.1 498.5 498.9 498.4 497.9 499.9 498.8 500.4 498.6 (a) Calculate the posterior distribution of when go () is the prior. (b) Calculate the posterior distribution of when g(u) is the prior. == (c) Calculate the posterior probability P(I = 0|y1,..., Y10). (d) Calculate the marginal posterior g(|y1,..., 910).