You are going to take a sample of 500 g blocks of cheese. You know they are approximately normal(μ, σ²), where σ² = 2². You have a precise normal(502, 1²) prior for μ because this is what the the process is set for. However, you have a nagging doubt that maybe the machine needs adjustment, so you decide to use a mixture prior. You let g₀(μ) be your precise normal(502, 1²) prior, you let g₁(μ) be a normal(502, 2²), and you let p₀ = .95. You take a random sample of ten blocks of cheese and weigh them. The measurements are

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