Download presentation

Presentation is loading. Please wait.

Published byRoberto Dyke Modified over 2 years ago

2
Project Storm Fury

3
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

4
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?

5
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

6
Total Property Damage ($ of 1969)

7
Maximum sustained winds over time

8
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.

9
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 )

10
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

11
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

12
The Seeding Decision

13
Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall Cumulative probability functions

14
Probabilities assigned to wind changes occurring in the 12 hours before hurricane landfall. Discrete approximation for five outcomes.

15
The seeding decision for the nominal hurricane $21.7M

16
The expected value of perfect information

17
The value of further tests

18
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

19
Adapting to Climate Change 1

20
Adapting to Climate Change 2

21
Adapting to Climate Change 3

22
Adapting to Climate Change 4

23
Adapting to Climate Change 5 Source: Oregon Environmental Quality Commission, Oregon Climate Change Adaptation Framework. December 10, 2010, Salem OR

Similar presentations

OK

AP Stats Chapter 7 Review Nick Friedl, Patrick Donovan, Jay Dirienzo.

AP Stats Chapter 7 Review Nick Friedl, Patrick Donovan, Jay Dirienzo.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 3d geometry maths class 11 Ppt on edge detection Ppt on stock market Ppt on campus recruiting systems Ppt on pf and esi in india Ppt on conference call etiquette participants Ppt on cost leadership strategy Ppt on council of ministers Ppt on micro channel heat exchanger Ppt on search engine project