# Project Storm Fury Review A stochastic variable has the following probability distribution: Values of X Probability distribution of X xP(X=x) \$1P(X=1)

## Presentation on theme: "Project Storm Fury Review A stochastic variable has the following probability distribution: Values of X Probability distribution of X xP(X=x) \$1P(X=1)"— Presentation transcript:

Project Storm Fury

Review A stochastic variable has the following probability distribution: Values of X Probability distribution of X xP(X=x) \$1P(X=1) = 1/3 \$2P(X=2) = 1/3 \$3P(X=3) = 1/3

Review What is X’s cumulative probability distribution? What is its expected value (  X =?) What is the Variance of X? What is its standard deviation? What is X’s cumulative probability distribution? What is its expected value (  X =?) What is the Variance of X? What is its standard deviation?

Review What is the Variance of X? Var X =   x i 2 P(X=x i ) -  2 = [1(1/3) + 2 2 (1/3) + 3 2 (1/3)] - 2 2 = (1/3 + 4/3 + 3) - 4 = 2/3 What is its standard deviation (  )?  X = SqrRoot(Var X ) = (2/3) 1/2 =.8165 What is the Variance of X? Var X =   x i 2 P(X=x i ) -  2 = [1(1/3) + 2 2 (1/3) + 3 2 (1/3)] - 2 2 = (1/3 + 4/3 + 3) - 4 = 2/3 What is its standard deviation (  )?  X = SqrRoot(Var X ) = (2/3) 1/2 =.8165

Total Property Damage (\$ of 1969)

Maximum sustained winds over time

Alternative Hypotheses H1, the “beneficial” hypothesis. The average effect of seeding is to reduce maximum sustained wind speed. H2, the “null” hypothesis. Seeding has no effect on hurricanes. No change is induced in maximum sustained wind speed. H3, the “detrimental” hypothesis. The average effect of seeding is to increase the maximum sustained wind speed. H1, the “beneficial” hypothesis. The average effect of seeding is to reduce maximum sustained wind speed. H2, the “null” hypothesis. Seeding has no effect on hurricanes. No change is induced in maximum sustained wind speed. H3, the “detrimental” hypothesis. The average effect of seeding is to increase the maximum sustained wind speed.

Mathematical expressions P(w' | H 2 ) = P(w) = f N (  100 ,  15.6  ) P(w' | H 1 ) = ƒ N (  85 ,  18.6  ) P(w' | H 3 ) = ƒ N (  110 ,  18.6  ) P(w' | H 2 ) = P(w) = f N (  100 ,  15.6  ) P(w' | H 1 ) = ƒ N (  85 ,  18.6  ) P(w' | H 3 ) = ƒ N (  110 ,  18.6  )

Probability density function for Debbie results P(69 , 85  | H1) = 1.50 x 2.14 =3.21 P(69 , 85  | H2) = 0.372 x 1.64 = 0.61 P(69 , 85  | H3) = 0.195 X 0.886 = 0.173 P(H1 | 69 , 85  ) = (3.21 x 1/3)/(3.21 x 1/3 + 0.61 x 1/3 + 0.173 x 1/3) =.81 P(H2 | 69 , 85  ) =.15 P(H3 | 69 , 85  ) =.04 P(69 , 85  | H1) = 1.50 x 2.14 =3.21 P(69 , 85  | H2) = 0.372 x 1.64 = 0.61 P(69 , 85  | H3) = 0.195 X 0.886 = 0.173 P(H1 | 69 , 85  ) = (3.21 x 1/3)/(3.21 x 1/3 + 0.61 x 1/3 + 0.173 x 1/3) =.81 P(H2 | 69 , 85  ) =.15 P(H3 | 69 , 85  ) =.04

Prior probabilities - pre and post Debbie P(H1) =.15 P(H2) =.75 P(H3) =.10 P(H1) =.15 P(H2) =.75 P(H3) =.10 P(H1) =.49 P(H2) =.49 P(H3) =.02.81(.15)/ [.81(.15) +.15(.75) +.04(.1)] =.51.15(.75)/ [.81(.15) +.15(.75) +.04(.1)] =.47.04(.1)/ [.81(.15) +.15(.75) +.04(.1)] =.02

The Seeding Decision

Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall Cumulative probability functions

Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall. Discrete approximation for five outcomes.

The seeding decision for the nominal hurricane \$21.7M

The expected value of perfect information

The value of further tests

Review 1. Decide whose benefits and costs count, and how much. This is typically referred to as determining standing. 2. Select the portfolio of alternative initiatives. 3. Catalog potential consequences and select measurement indicators. 4. Predict quantitative consequences over the life of the project for those who have standing. 5. Monetize (attach cash values to) all the predicted consequences. 6. Discount for time to find present values. 7. Sum up benefits and Costs for each initiative and Perform sensitivity analysis underlying key assumptions 1. Decide whose benefits and costs count, and how much. This is typically referred to as determining standing. 2. Select the portfolio of alternative initiatives. 3. Catalog potential consequences and select measurement indicators. 4. Predict quantitative consequences over the life of the project for those who have standing. 5. Monetize (attach cash values to) all the predicted consequences. 6. Discount for time to find present values. 7. Sum up benefits and Costs for each initiative and Perform sensitivity analysis underlying key assumptions