Anything would help, I would like to have a step by step solution, to show how to do it ,especially part a. Appreciate!

Consider the Bayesian network in Figure 1. The network is similar to a HMM, with boolean state variables Xt, t = 0, 1, 2, 3, and evidence variables Et, t = 1, 3, but evidence E2 is missing. The state transition probabilities are given by P(Xt+1 = T|Xt = T) = 0.75 and P(Xt+1 = T|Xt = F) = 0.25, and the evidence probabilities are given by P(Et = T|Xt = T) = 0.8 and P(Et = T|Xt = F) = 0.4. Let E1 = T and E3 = F. Let P(X0 = T) = 0.2;

(a) Compute P(X2 = T|E1 = T, E3 = F).

(b) Assume the missing evidence E2 becomes available, and E2 = T. Then, making use of the formula in (a), the evidence probabilities and Bayes rule, compute P(X2 = T|E1 = T, E2 = T, E3 = F).

(c) Rewrite the Bayesian network above as a factor graph and use the sum-product rules for message-passing to derive the backward recursion formula in smoothing. Specialize to the case P (X2| e3, e4 ).

Xo X3 Ea Xo X3 Ea