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Unformatted text preview: Probability Trees Constructing a Probability Tree A probability tree models a stochastic process, i.e. a sequence of probabilis- tic experiments. Each level in the tree corresponds to a different stage in the stochastic process (i.e. a different experiment in the process). Each branch in a probability tree has a probability associated with it. The branches correspond to events which might occur when the experiment corre- sponding to that level of the tree is performed. The probability associated with a branch is the probability that the corresponding event occurs, conditional on all events corresponding to branches leading to the current branch having occurred. That is, the probability associated with a branch in the tree is the probability that this branch will be taken, given that we arrive at the point in the tree from which we could take this branch. Thus, after the first level, all probabilities on branches in a probability tree are conditional probabilities . Consider the stochastic process described by: Perform an experiment and observe which of events A , B or C oc- cured, then perform another experiment and observe whether or not event D occurs. The probability tree which models this stochastic process has 2 levels of branch- ing - one for each experiment. On the first level, corresponding to the first experiment, there are 3 branches - because we observe which of events A or B or C occurred. That is, there is a branch for each possible outcome (or eventoccurred....
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