Suppose that f$($x $|\backslash$theta $,\backslash$sigma $)$ is normal with mean $\backslash$theta and standard deviation $\backslash$sigma $.$ The Jeffrey's prior for $\backslash$theta and $\backslash$sigma are shown below. a$.$ What is the posterior distribution $\backslash$pi $(\backslash$theta $|$ x$,\backslash$sigma $)$ using the Jeffrey's prior below:

p$(\backslash$theta $)=1,\backslash$theta in R

b$.$ What is the posterior distribution $\backslash$pi $(\backslash$sigma $|$ x$,\backslash$theta $),$ using the Jeffrey's prior below:

p$(\backslash$sigma $)=1/\backslash$sigma $^\text{'},\backslash$sigma $>0$