2111 maximum likelihood ml decision rule the ml

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Unformatted text preview: trix might be the following: H1 H0 X=0 X=1 X=2 X=3 0.0 0.1 0.3 0.6 0.4 0.3 0.2 0.1 In practice, the numbers in the table might be based on data accumulated from past experiments when either one or the other hypothesis is known to be true. As mentioned above, a decision rule specifies, for each possible observation, which hypothesis is declared. A decision rule can be conveniently displayed on the likelihood matrix by underlining one entry in each column, to specifying which hypothesis is to be declared for each possible value of X. An example of a decision rule is shown below, where H1 is declared whenever X ≥ 1. For example, if X = 2 is observed, then H1 is declared, because the entry underlined under X = 2 is in the H1 row of the likelihood matrix. X=0 X=1 X=2 X=3 underlines indicate ← the decision rule H1 0.0 0.1 0.3 0.6 used for this example. H0 0.4 0.3 0.2 0.1 Since there are two possibilities for which hypothesis is true, and two possibilities for which hypothesis is declared, there are four possible outcomes: Hypothesis H0 is true and...
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