hw3 - EE178\/278A Probabilistic Systems Analysis Spring 2014(Tse Homework 3 Due April 25 in class 1 Probability models Suppose a document has n letters

hw3 - EE178/278A Probabilistic Systems Analysis Spring...

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EE178/278A: Probabilistic Systems Analysis, Spring 2014 (Tse) Homework 3 Due April 25, in class 1. Probability models Suppose a document has n letters and you are told the probability that each letter is typed wrongly is p . (a) Explain why there is not enough information to calculate the probability that the entire document is typed correctly. (b) Find the smallest possible value for this probability in terms of p and specify the probability assignment to the underlying sample space for which this smallest value is achieved. (c) Let n = 2 . Suppose you are told additionally that q 1 is the conditional probability that the second letter is typed wrongly given that the first letter is typed wrongly, and q 2 is the conditional probability that the second letter is typed wrongly given that the first letter is typed correctly. Do we now have a complete probability assignment on all the outcomes of the experiment? If so, give it. (d) What constraint(s) do q 1 and q 2 have to satisfy? (e) Under what values of q 1 and q 2 is the probability that the document is typed correctly (i) equal to,