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there are three basic problems in the hidden markov model for simplicity we are going to use the coin flip example but later on in the bioinformatics application section you can see how this is being used in real problems the three problems in hidden markov model the first one is given that the parameters for the hidden markov models are all provided how do we compute the likelihood of a particular observation for example if we know there is a fair coin bias coin if we know the initial probability and transition probability and emission probability can we calculate the probability of seeing a string of coin flips such as head tail tail head head head tail and so for that there are two computational procedures that can achieve this answer but first let's think about how we want to solve this problem so let me remind you again the initial probability transition probability of this hidden markov model so supposedly we know the state sequence um so the if the observation is this and if we know that the coins that are used underneath each coin flip is the following ff you know bias and and so on um we can easily calculate this based on the transition probability from a fair coin to get to a head is 50 a fair coin to a tail is 50 buy is going to get a tail is 20 and bias uh coin to get ahead is 80 right so very easy you can calculate this if i give you another coin like a string of coin order um which have these two coins changed we can calculate the probability again which will give you a different result from the the the past above but it's a very easy calculation so you can see given each path you can easily calculate the probability using the emission probability um of the two coins then the question is what is the probability of seeing this path let's look at the first pass in order to use this particular order of coins we say oh well first we have to pick a fair coin so that's the initial probability of 0.4 but also we have a transition probability from a fair coin to another fair coin from the fair to bias bias to fair fair to fair fair to biased bias to bias and so that you check the transition probability and you can calculate this quite easily if now look at the second pass that we're given um again we have to start using this bias coin that's from the initial probability and then after that you just check the transition probability from one coin to the next you can calculate this probability and so you can see here it's also fairly easy every given path has its own probability of occurring knowing the hidden markov model parameters therefore the probability of seeing this particular coin flip order is to sum over...