You are trying to diagnose whether your computer is broken or not. On a given day, your computer's hidden state is either broken or working. Each day you make one of the following observations: blue-screen, slow, or snappy, depending on the state of your computer. You decide to use the following HMM to model your daily observations. Note, "Emission Distribution" is another way to descibe the "Sensor Distribution".

Intial Distribution
State P(X1)
Working 0.9
Broken 0.1

Transition Distribution
State Next State P(Xt+1| Xt)
Working Working 0.9
Working Broken 0.1
Broken Broken 1.0
Broken Working 0.0

Emission Distribution
State Observation P(Ot|Xt)
Wroking Snappy 0.7
Wroking Slow 0.2
Wroking Blue-screen 0.1
Broken Snappy 0.1
Broken Slow 0.4
Broken Blue Screen 0.5

Required:
a. What is the posterior distribution of X1, your computer's state on day one, given the observation (slow) on day 1? In other words, find P(X1| E1 = slow).
b. What is the posterior distribution of X2, your computer's state on day two, given the observation sequence (slow, slow)?