8. MDPS Consider an MDP where you have chosen a policy to use and are starting from the start state. Explain how you can use the tools from this course to calculate the probability distribution over states three steps in the future.

MATLAB Project In a communication tower, let k be the number of active (non-silent) speakers in a group of six non-interacting (i.e., independent) speakers. Suppose that a speaker is active with probability 1/4. Compute the following 1. Using the appropriate mathematical formulas to find the probability that the number of active speakers is greater than three. 2. Using MATLAB to simulate the random experiment and validate the results evaluated in 1. 3. Plot the probability density function of the random variable k.

For a HMM, the hidden states are {bull, bear}, the observation variables are {rise, fall}, the initial state probability distribution is [0.5 0.5]¹, the transition probability distribution A is [0.4 0.7; 0.6 0.3], and the observation probability distribution B is [0.8 0.1;0.2 0.9]. If the observation sequence is {fall fall rise}, please show the computation procedure for estimating the most likely state sequence?

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