The laplace method, Mathematics

The Laplace method

Laplace method employs all the information by assigning equal probabilities to the possible payoffs for every action and then selecting such alternative which corresponds to the maximum expected pay off

Illustration

A company is considering investing in one of three investment opportunities A, B and C under specific economic conditions. The payoff matrix for this condition is economic situation

 

Investment opportunities

1 £

2 £

3 £

A

5000

7000

3000

B

-2000

10000

6000

C

4000

4000

4000

 

Find out the best investment opportunity by using the given criteria:

i.     Maximax

ii.     Maximin

iii.    Minimax

iv.   Hurwicz as Alpha = 0.3

Solution

                                          Economic condition

Investment opportunities

1 £

2 £

3 £

Minimum £

Maximum £

A

5000

7000

3000

3000

7000

B

-2000

10000

6000

-2000

10000

C

4000

4000

4000

4000

4000

 

i.        By using the Maximin rule Highest minimum = £ 4000

Select investment C

ii.      By using the Maximax rule Highest maximum = £ 10000

Select investment B

iii.    Minimax Regret rule

 

 

1

2

3

Maximum regret

A

0

3000

3000

3000

B

7000

0

0

7000

C

1000

6000

2000

6000

 

Select the minimum of the maximum regret that is £3000

Select investment A

iv.     Hurwicz rule: expected values

For A (7000 x 0.3) + (3000 x 0.7) = 2100 + 2100 = £4200

For B (10000 x 0.3) + (-2000 x 0.7) = 3000 + 1400 = £ 1600

For C (4000 x 0.3) + (4000 x 0.7) = 1200 + 2800 = £ 4000

Best outcome is £ 4200 select investment A

Posted Date: 2/19/2013 2:48:04 AM | Location : United States







Related Discussions:- The laplace method, Assignment Help, Ask Question on The laplace method, Get Answer, Expert's Help, The laplace method Discussions

Write discussion on The laplace method
Your posts are moderated
Related Questions
HOW DO YOU DO BAR DIAGRAMS ANDESTIMATE IT WITH PERCENTS

you are in charge of making punch for an upcoming dance. the punch recipe makes 5 cups of punch by making 3 cups of cranberry juice with 2 cups of apple juice. What is the ratio of

Explain Adding Rational Expressions with Different Denominators When you add or subtract fractions or rational expressions that have different denominators, you must first find

Let f : R 3 → R be de?ned by:                                        f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y

Universal set The term refers to the set which contains all the elements such an analyst wishes to study.  The notation U or ξ is usually used to denote universal sets.

We have to enclose a field along with a fence. We contain 500 feet of fencing material & a building is on one side of the field & thus won't require any fencing.  Find out the dime

Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is

1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.

finding distance using circumference

Definition : A function f ( x ) is called differentiable at x = a if f ′ ( x ) exists & f ( x ) is called differentiable onto an interval if the derivative present for each of the