Let y 1 , y 2 , y 3 , y n represent a random sample of size n selected from a normal probability distribution with unknown mean and variance 2 1 Then the sample mean, y , has a normal distribution with mean and variance 2 1 n Assume that the prior distribution for is a normal distribution with a me...

A Bayesian decision rule for testing Ho o versus Ha o would involve using the posterior distribution ...

Let y 1 , y 2 , y 3 , ..... y n represent a random sample

Question:

Let y₁, y₂, y₃, ..... y_n represent a random sample of size n selected from a normal probability distribution with unknown mean μ and variance σ² = 1. Then the sample mean, y̅ , has a normal distribution with mean μ and variance σ² = 1/n. Assume that the prior distribution for μ is a normal distribution with a mean of 5 and a variance of 1. Find a Bayesian decision rule for testing H_o: μ = μ_o versus H_a: μ < μ_o. Use the posterior distribution, g(μ Ι y̅).