A statistician has to decide on the basis of one observation whether the parameter 𝜃 of a Bernoulli distribution is 1/4 or 1/2 ;
his loss ( a penalty that is deducted from his fee ) is $80 if he is wrong.
(a) Construct a table showing the four possible values of the loss function.
(b) List the four possible decision functions.
(c) Construct a table showing all the values of the corresponding risk function.
(d) Find the decision function that is the best according to the minimax criterion.
(e) Find the decision function that is the best according to the Bayes criterion if the probabilities assigned to 𝜃 = 1/4 and 𝜃 = 1/2 are, respectively, 2/3 and 1/3.
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