Consider four multi-valued random variables A (age), H (height), W (weight), and S (salary). We know that S is independent of H and W; A, H, and W are NOT independent of one another. We are provided the probability tables/functions for the following six joint, marginal, and conditional probabilities.

The six probabilities: P(S) P(W, A) P(H,S) P(S|A) P(A|W) P(H|W)

For example, we are told: P(W=light) = 0.2, P(W=medium)=0.5, P(W=heavy)=0.3 P(H=short,S=10K)=0.03, P(H=medium,S=10K)=0.12 , ... P(H=tall , S=10K)=0.08

We are not provided any other probability tables; for example, we are not given values for: P(H=short) or P(W=psych, S=200K)

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(S) = _h ( = , ) (we sum over values of P(H,S) which are known to get P(S))

a) P(A=old, W=medium, S=50K)

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

c) P(W=heavy, A=mid-age)

d) P(H=tall, W=light)

e) P(W=medium)

f) P(A=young|S=10K)