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

Transcribed Image Text:

249 258 255 261 259 254 261 256 253 254