# Update the Emission Matrix in Baum-Welch Algorithm for HMM: Numerical Example

I am trying to manually implement a numerical example of the Baum-Welch Algorithm from the following Tutorial https://handwiki.org/wiki/Baum%E2%80%93Welch_algorithm. I do not understand how the Emission Matrix is updated. Can anyone help me calculate the following values in the New Emission Matrix (Estimates)

New Emission Matrix (Estimates)\

    No Eggs    Eggs


State1 0.0404 0.8769
State2 1.0000 0.7385

This is my attempt to calculate the estimates if No Eggs(N) came from State1(S1): I assumed that this automatically means that Egg(E) came from State2(S2).
S1S2-->NE 0.20.30.50.2 = 0.006
S2S2-->EE 0.8
0.20.70.2 = 0.0224
S2S1-->EN 0.80.20.3*0.3 = 0.0144
Total = 0.006 + 0.0224 + 0.0144 = 0.0428
Estimate = 0.0428/0.2730 = 0.15678 with 0.273 being the sum of highest probability of the sequence.
My result is different from 0.0404 as given in the tutorial.

In addition how do you get the other estimates for the emission matrix when N and E came from S2?