Driven by the advances in sensory device and wireless network, the smart asthma management

$($SAM$)$ system has been established. The SAM system is illustrated in the figure below.

Remote Patient Monitoring

$($Smart Asthma Management: SAM$)$

The SAM system monitors each asthma patient through a sensor attached to his$/$her personal

rescue inhaler. By analyzing the rescue inhaler usage pattern, the SAM system generates an

alarm and sends a text message to the patient's mobile phone when a sudden exacerbation was

detected for that specific patient. The patient then seeks for a clinical intervention by calling

his$/$her physician. Of course, independent from the SAM system, the patient may visit the clinic

based on his$/$her own perception of the current asthma control status $($i$.$e$.,$ self$-$detection$).$

There are a few well$-$known drawbacks of the SAM system. First, due to various reasons, it is

possible that the patient may ignore the alert intentionally $($the non$-$adherence issue$).$ Second, the

SAM system cannot detect the bad asthma condition with $100\%$ accuracy $($false alarm and

misdetection$).$ The problems are reflected in the probabilistic graphical model below.

Intervention $($I$)$ indicates whether the patient went through a clinical consultation or not. Based

on the graphical model and partial probabilistic information, please compute the following

probabilities.

PLEASE ANSWER ALL $10$ QUESTIONS!!

$1.$ P$($C$=$Good, A$=$Yes, S$=$No$,$ I$=$Yes$)$

$2.$ P$($A$=$Yes $|$ S$=$No$)$

$3.$ P$($A$=$No$)$

$4.$ P$($S$=$Yes$)$

$5.$ P$($I$=$Yes$)$

$6.$ P$($I$=$Yes $|$ A$=$Yes$)$

$7.$ P$($I$=$Yes $|$ S$=$Yes$)$

$8.$ P$($A$=$Yes, S$=$Yes$)$

$9.$ P$($I$=$Yes $|$ C$=$Bad$)$

$10.$ P$($I$=$Yes $|$ C$=$Good$)$