# Question: A statistician has to decide on the basis of two

A statistician has to decide on the basis of two observations whether the parameter θ of a binomial distribution is 1/4 or 1/2 ; his loss (a penalty that is deducted from his fee) is $ 160 if he is wrong.

(a) Construct a table showing the four possible values of the loss function.

(b) List the eight possible decision functions and construct a table showing all the values of the corresponding risk function.

(c) Show that three of the decision functions are not admissible.

(d) Find the decision function that is best according to the minimax criterion.

(e) Find the decision function that is 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.

(a) Construct a table showing the four possible values of the loss function.

(b) List the eight possible decision functions and construct a table showing all the values of the corresponding risk function.

(c) Show that three of the decision functions are not admissible.

(d) Find the decision function that is best according to the minimax criterion.

(e) Find the decision function that is 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.

**View Solution:**## Answer to relevant Questions

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