QUESTION SIX

(a)Suppose that a decision is faced with three decision alternatives and four states of nature. The following profit payoff table is constructed:

Alternatives State of Nature

S1 S2 S3 S4

1 18 12 15 8

2 15 14 10 11

3 13 16 19 15

Assuming that the decision maker has no knowledge about the probabilities of occurrence of the four states of nature, find the decisions to be recommended under each of the following criteria:

1. Maximin criterion
2. Maximax criterion
3. Minimax Reject criterion
4. Hurwicz criterion with = 0.6

(b)An insurance company provides customers with both auto and home insurance policies. For a particular customer, is the deduction on his or her auto policy and Y is the deduction on the home policy. Possible values of are K100 and K250, and for Y are

K0, K100 and K200. The joint probability density function for (,Y) is given by the following table:

Y K100 K250

K0 0.20 0.05

K100 0.10 0.15

K200 0.20 0.30

1. Find the probability for a randomly selected policy holder having a K100 deduction on the auto insurance and a K200 deduction on the home insurance.
2. Find the probability that a randomly selected policy holder has a home deduction of at least K100.
3. Are the random variables and Y independent? Explain your answer.
4. If we look only at those insurance customers selecting the lowest auto mobile insurance deduction (K100), what is the probability that a randomly selected\ customer will also select the lowest home deduction (K0).
5. Compute the correlation coefficient of and Y