1. Consider four multi-valued random variables A (age), O (oxygen level), S (salary), and T (body temperature). We know that S is independent of O and T; A is independent of T ; O and T are NOT independent of one another. We are provided the probability tables/functions for the following six joint, marginal, and conditional probabilities.

The five probabilities: P(S) P(A, T) P(S, T) P(S|A) P(O|T)

For example, we are told: P(S=$25K) = 0.3, P(S=$50K)=0.3, P(S=$75K)=0.25, P(S=$100K)=0.15 P(O=hi | T=hi)=0.2, P(O=medium | T=hi)=0.7 , ... P(O=low | T=low )=0.1

We are not provided any other probability tables; for example, we are not given values for: P(T=hi) or P(A=old, O=low)

Explain how to combine the six probabilities from above (and the knowledge that S is independent) to compute each probability below, or write "not possible" if it is not possible. For example: P(A) = (, = )

a) P(A=mid-age|S=$25K)

b) P(O=medium, T=low)

c) P(A=mid-age, S=$100K, T=medium)

d) P(H=medium | W=heavy, A=old)

e) P(A=old, S=$75K, T=hi)

f) P(A=young)