A statistician has to decide upon the basis of two observations whether parameter theta of binomial distribution is 1/4 or 1/2; his loss ( a penalty that is deducted from his fee) is $160 if he is wrong.
Develop a table showing four possible value of the loss function
Mention the eight possible decision function
Discuss that three of the decision function aren't admissible
Determine the decision that is best accoring to minimax criterion
Determine the decision function that is best according to base criterion if the probabilities assigned to theta =1/4 an theta =1/2 are respectively, 2/3 and 1/3