Unformatted text preview: uires the computation of joint probabilities such as P ({X =
1} ∩ H1 ). For brevity we write this probability as P (H1 , X = 1). Such probabilities cannot be
deduced from the likelihood matrix alone. Rather, it is necessary for the system designer to assume
some values for P (H0 ) and P (H1 ). Let the assumed value of P (Hi ) be denoted by πi , so π0 = P (H0 )
and π1 = P (H1 ). The probabilities π0 and π1 are called prior probabilities, because they are the
probabilities assumed prior to when the observation is made. 2.11. BINARY HYPOTHESIS TESTING WITH DISCRETETYPE OBSERVATIONS 57 Together the conditional probabilities listed in the likelihood matrix and the prior probabilities determine the joint probabilities P (Hi , X = k ), because P (Hi , X = k ) = πi pi (k ). The joint
probability matrix is the matrix of joint probabilities P (Hi , X = k ). For our ﬁrst example, suppose
π0 = 0.8 and π1 = 0.2. Then the joint probability matrix is given by
H1
H0 X=0 X=1 X=2 X=3
0.00
0.02
0.0...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.
 Spring '08
 Zahrn
 The Land

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