We are taking a random sample from the normal(, 2 ) distribution where we know the

We are taking a random sample from the normal(μ, σ²) distribution where we know the standard deviation σ = 4. Suppose that our prior experience in similar situations leads us to believe that the prior distribution should be normal(255; 4²). However, we consider that the prior experience may have been under different circumstances, so we decide to use a mixture prior where g₀(μ) is the normal(255, 4²) and g₁(μ) is the normal(255, 12²) distribution, and the prior probability P(I = 0) = .95.
We take a random sample of n = 10 observations. They are

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