d$)$ Assume that the above Bayesian network is an I$-$map for the distribution that partly is "revealed" in the following table. Use the probabilities from the following table to prove your claims in part c$.$

$\backslash$table$[[$Age$,\backslash$table$[[$Underlying$],[$disease$]],\backslash$table$[[$Curtent$],[$state$]],$probability$],[$Young$,$Yes,Bad,$0\mathrm{.}25],[$Young$,$No$,$Good,$0\mathrm{.}25],[$Old$,$Yes,Good,$0\mathrm{.}25],[$Old$,$No$,$Good,$0\mathrm{.}25]]$

Problem $3$

a$)$ Is age independent of hospitalization?

What if we are given information about current state?

b$)$ Is medical history independent of current state? What if we are given information about underlying disease?

c$)$ Is age independent of underlying diseases? What if we are stven information about current state?

What if no information is given about current state but information about urgency of hospitalization is given

instead?

d$)$ Assume that the above Bayesian network is an I$-$map for the distribution that partly is "revealed" in the

following table. Use the probabilities from the following table to prove your claims in part c$.$