In the following transition probability matrix. A) In addition to plotting the state transition diagram, Classify its states (for nodes 1, 2, 3, and 4). B) Is this chain ergodic? C) Assuming starting from node one, get the value 7(1) = ? for t= 2, t=0. 1/4 1/2 1/4 Q= 1/3 1/3 1/3 1/2 1/4 1/4 0 0 1/2 1/2

Let Tmn be a BTTB matrix with a generating function f(x, y) ∈C2π×2π. Let λmin(Tmn) and λmax(Tmn) denote the smallest and largest eigenvaluesof Tmn, respectively. Then we havefmin ≤ λmin(Tmn) ≤ λmax(Tmn) ≤ fmax,where fmin and fmax denote the minimum and maximum values of f(x, y), respectively. In particular, if fmin > 0, then Tmn is positive definite.

Construct the HMM  (Hidden Markov Model) for the following sequences

Axl & 21 Bxl Figure 3 (e) The circuit in figure 3shows a special relationship, state in what other way this logic circuit could be written using Boolean algebra. For each of the following Boolean expressions, state whether they are in sum-of-products (SoP) form. (f) AD(B C) +AD (g) ABC + ABC (h) (A + C)(B + D)(B+ C)(A+ D + E) (i) ABD + BC