5. A statistical model for the data y = (y1,.. (Y1,, y8) is a random sample from normal distribution N(μ, 1) i.e 1 ƒ (y | μ) = (2m)*/2 xp(-Σ 1 Σ (Yi - µ)²) 2 where μ is a real parameter and variance is known number 1. Prior p(μ) is chosen to be the density of the normal distribution N(0, 22), where the variance is a known positive number 4. Show that the posterior p(µ | y) follows normal distribution N(μ₁, 0). What are the numbers μ₁ and σ?? The simplest way is to apply the proportionality p(µ | y) ∞ p(µ)f(y | µ).

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