MATHEMATICAL & STATISTICAL TECHNIQUES
			SECTION 2 : STATISTICS
			Unit 5 : DECISION THEORY
			COURSE OF ACTION : ALTERNATIVES OR CHOICES (A1,A2 , A3 and so on)
			STATE OF NATURE : OUTCOMES OR SITUATIONS  ( S1,S2 or E1 or E2 and so on)
			PAY OFF MATRIX : NET PROFIT TO THE DECISION MAKER
			PAY OFF MATRIX
				State of Nature
			Alternative	S1	S2	S3
			A1
			A2
			A3
			A4
			A5
				OR
				A1	A2	A3	A4	A5
			S1
			S2
			S3
			S4
			REGRET MATRIX (OPPORTUNITY LOSS MATRIX)
				State of Nature
			Alternative	S1	S2	S3
			A1
			A2
			A3
			A4
			A5
			PART A : DECISION MAKING UNDER UNCERTAINITY
			METHODS FOR DECISION MAKING UNDER UNCERTINITY (VIMP)
			1)WHEN PAY OFF MATRIX IS GIVEN
			THREE METHODS/ CRITERIA
		1	MAXIMAX
		2	MAXIMIN
		3	LAPLACE
			2)REGRET TABLE IS GIVEN
			ONE METHOD
		1	MINIMAX
			1)WHEN PAY OFF MATRIX IS GIVEN
			EXAMPLE 1
			FIND THE BEST DECISION USING
			THREE METHODS/CRITERIA
		1	MAXIMAX
		2	MAXIMIN
		3	LAPLACE
			PAY OFF MATRIX
			Course of Action	State of Nature
			Alternative	S1	S2	S3	Maximum	Minimum	AVERAGE						95	25	68.333
			A1	25	85	95	95	25	68.33						60	0	33.333
			A2	40	0	60	60	0	33.33						65	30	50
			A3	65	30	55	65	30	50.00						MAX = 95	MAX = 30	MAX =68.33
							Maximum= 95	Maximum =30	Maximum =68.33
			BEST DECISION BY  CRITERIA
			SELECT A1 BY MAXIMAX CRITERIA
			SELECT A3 BY MAXIMIN CRITERIA
			SELECT A1 BY LAPLACE CRITERIA
			EXAMPLE 2
					PAY OFF MATRIX
			Course of Action	State of Nature
			Alternative	S1	S2	S3	S4	Maximum	Minimum		Average
			A1	35	100	38	75	100	35		62
			A2	58	95	105	55	105	55		78.25
			A3	45	30	91	100	100	30		66.5
								Maximum = 105	Maximum = 55		Maximum = 78.25
			BEST DECISION BY  CRITERIA
		1	MAXIMAX
		2	MAXIMIN
		3	LAPLACE
			SELECT A2 BY MAXIMAX CRITERIA
			SELECT A2 BY MAXIMIN CRITERIA
			SELECT A2 BY LAPLACE CRITERIA
			EXAMPLE 3
				PAY OFF MATRIX
			Course of Action	State of Nature			Maximum	Minimum	Laplace
			Alternative	S1	S2	S3
			A1	65	0	45	65	0	36.67
			A2	0	55	60	60	0	38.33
			A3	76	-15	80	80	-15	47.00
							Maximum =80	Maximum = 0	Maximum = 47
			BEST DECISION/ OPTIMAL DECISION BY  CRITERIA
		1	MAXIMAX
		2	MAXIMIN
		3	LAPLACE
			BEST DECISION/ OPTIMAL DECISION
			SELECT A3 BY MAXIMAX CRITERIA
			SELECT  A1 or A2 BY MAXIMIN CRITERIA
			SELECT  A3 BY LAPLACE CRITERIA
			EXAMPLE 4
			Course of Action	Alternatives	A1	A2	A3	A4
			State of Nature	S1	65	40	60	20
				S2	15	50	-20	40
				S3	45	60	70	50
			Course of Action	State of Nature			Maximum	Minimum	Average
			Alternatives	S1	S2	S3
			A1	65	15	45	65	15	41.67					65	15	45	65	15	41.667
			A2	40	50	60	60	40	50.00					40	50	60	60	40	50
			A3	60	-20	70	70	-20	36.67					60	-20	70	70	-20	36.667
			A4	20	40	50	50	20	36.67					20	40	50	50	20	36.667
							Maximum =70	Maximum =40	Maximum = 50
			BEST DECISION/ OPTIMAL DECISION BY  CRITERIA
			MAXIMAX
			MAXIMIN
			LAPLACE
			BEST DECISION/ OPTIMAL DECISION
			SELECT   A3 BY MAXIMAX CRITERIA
			SELECT  A2 BY MAXIMIN CRITERIA
			SELECT   A2 BY LAPLACE CRITERIA
			DIV A
			FIND THE REGRET TABLE AND THE BEST DECISION USING MINIMAX METHOD
			CRITERIA FOR DECISION IS MINIMAX
	EX 1
			PAY OFF MATRIX					TO MAKE REGRET TABLE
	STEP 1		Course of Action	State of Nature				STEPS
			Alternative	S1	S2	S3		1) FIND THE MAXIMUM VALUE IN EACH STATE OF NATURE
			A1	25	85	95		2) SUBSTRACT THIS MAXIMUM VALUE FROM EACH VALUE UNDER THE SAME STATE OF NATURE
			A2	40	0	60
			A3	65	30	55		After making Regret table
								3) Select Max for each Alternative (Amongst the State of Nature)
								4) Then choose Minimum value amongst this
	STEP 2			REGRET TABLE
			Course of Action	State of Nature
			Alternative	S1	S2	S3	MAXIMUM
			A1	40	0	0	40
			A2	25	85	35	85
			A3	0	55	40	55
							MINIMUM = 40
	STEP 3		BEST DECISION USING MINIMAX REGRET CRITERIA IS
			TO SELECT   A1
			DIV  D
	EX 2		FIND THE BEST DECISION USING MINIMAX CRITERIA
					PAY OFF MATRIX
			Course of Action	State of Nature
			Alternative	S1	S2	S3	S4
			A1	35	100	38	75
			A2	58	95	105	55
			A3	45	30	91	100
			SOLUTION
					REGRET MATRIX
			Course of Action	State of Nature
			Alternative	S1	S2	S3	S4	MAXIMUM
			A1	23	0	67	25	67
			A2	0	5	0	45	45
			A3	13	70	14	0	70
								MINIMUM = 45
			BEST DECISION USING MINIMAX CRITERIA IS
			TO SELECT   A2 BY MINIMAX CRITERIA
			EXAMPLE 3
			Find the best decision by Using
			MAXIMAX
			MAXIMIN
			LAPLACE
			MINIMAX REGRET METHOD
					PAY OFF MATRIX
			Course of Action	State of Nature
			Altenative	S1	S2	S3	S4	Maximum	Minimum	Average	Average
			A1	25	30	150	80	150	25		71.25
			A2	45	120	50	130	130	45		86.25
			A3	60	100	0	-10	100	-10		37.5
			A4	40	60	65	25	65	25		47.5
								MAXIMUM =150	MAXIMUM = 45		Maximum =86.25
			Find the best decision using
		1	MAXIMAX
		2	MAXIMIN
		3	LAPLACE
		4	MINIMAX REGRET CRITERIA
		1	BEST DECISION USING MAXIMAX CRITERIA IS A1
		2	BEST DECISION USING MAXIMIN CRITERIA IS A2
		3	BEST DECISION USING LAPLACE CRITERIA IS A2
			BEST DECISION/ OPTIMAL DECISION
			SELECT   A1 BY MAXIMAX CRITERIA
			SELECT   A2 BY MAXIMIN CRITERIA
			SELECT   A2 BY LAPLACE CRITERIA
					PAY OFF MATRIX
			Course of Action	State of Nature
			Altenative	S1	S2	S3	S4
			A1	25	30	150	80
			A2	45	120	50	130
			A3	60	100	0	-10
			A4	40	60	65	25
					REGRET MATRIX
			Course of Action	State of Nature
			Altenative	S1	S2	S3	S4	MAXIMUM
			A1	35	90	0	50	90
			A2	15	0	100	0	100
			A3	0	20	150	140	150
			A4	20	60	85	105	105
								MINIMUM = 90
			BEST DECISION IS TO SELECT   A1 BY MINIMAX CRITERIA
			EXAMPLE 4
			Find the best decision using
			MAXIMIN
			MAXIMAX
			LAPLACE
			MINIMAX REGRET CRITERIA
				PAY OFF MATRIX
			STATE OF NATURE	A1	A2	A3
			S1	25	-10	-125
			S2	400	440	400
			S3	650	740	750
			COURSE OF ACTION	S1	S2	S3
			A1	25	400	650
			A2	-10	440	740
			A3	-125	400	750
				PAY OFF MATRIX
				STATE OF NATURE
			COURSE OF ACTION	S1	S2	S3	Minimum	MAXIMUM	Average
			A1	25	400	650	25	650	358.3333333
			A2	-10	440	740	-10	740	390
			A3	-125	400	750	-125	750	341.6666667
							MAX= 25	MAX = 750	MAX = 390
			BEST DECISION/ OPTIMAL DECISION
			SELECT   A1 BY MAXIMIN CRITERIA
			SELECT   A3 BY MAXIMAX CRITERIA
			SELECT   A2 LAPLACE CRITERIA
				PAY OFF MATRIX
				STATE OF NATURE
			COURSE OF ACTION	S1	S2	S3
			A1	25	400	650
			A2	-10	440	740
			A3	-125	400	750
				REGRET MATRIX
				STATE OF NATURE
			COURSE OF ACTION	S1	S2	S3	MAXIMUM
			A1	0	40	100	100
			A2	35	0	10	35
			A3	150	40	0	150
							Minimum = 35
			BEST DECISION IS TO SELECT   A2 BY MINIMAX CRITERIA
			DIV C