Bayesian Stats: Full Conditional Probability Help

#1
Hi guys!

So okay this week in class we started learning about Gibbs sampling and full conditional probabilities. I seemed to understand all the examples in class on how to derive full conditional probabilities, but got to the hw and was completely lost. I feel that the reason for this is that he added a covariate and the form looked different here I will show you:

Class example: p(a,b,c,d|X) (prop) L(X|a.b,c,d)(p(a)p(b)p(c)p(d)
full cond prob for a would be: p(a|X,b,c,d) (prop) L(X|a.b,c,d) p(a)
*(prop) stands for proportion symbol

So I understood this and how to derive the other three conditional probabilities but here is the hw:

A: p(yi|xi, Bo, B1)p(Bo)(pB1)
where yi is an observation of the response variable and xi is the corresponding covariate (ahh??)

for this is derived these two probabilities:

1) L(yi|xi, Bo, B1)p(Bo)
2) L(yi|xi, Bo, B1)p(B1)

I have no idea if these are correct, but this is all I could think to do

B: p(y3|a3)p(a3|a2)p(y2|a3)p(a2|a1)p(y1|a1)p(a1)

this was part B and I had no clue what to do


I hope I explained myself well and if you need me to clarify anything I will certainly do my best!

Any help or tips of even helpful links would be so wonderful.

Thanks!