homework3 for Bayesian inference

 

(1)    Θ|X ~N(169,11 ²)   , so the 95% HDR for this distribution is [169-1.96*11,169+1.96*11], that is[147.44,190.56]

(2)     

 

If l(θ|x) ∞ exp{1/-2φ*(x-θ)²} ,for different data ,the shapes of the likelihood function are

 

We can see the shapes are same ,but the locations are changed.

 

Let φ = 1/θ, the shapes of l(φ|x) are