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,

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