(1)    Θ|X ~N(169,112)  , so the 95% HDR for this distribution is [169-1.96*11,169+1.96*11], that is[147.44,190.56]
(2)    <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

 

 

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

homework3 for Bayesian inference
 
We can see the shapes are same ,but the locations are changed.

 

Let φ = 1/θ, the shapes of l(φ|x) are
homework3 for Bayesian inference