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Unformatted text preview: 27.5 253.5 260.5 272.0 281.0 282.5 293.0 308.0 315.0 321.0 0.029 0.057 0.086 0.114 0.143 0.171 0.200 0.229 0.257 0.286 0.314 0.343 0.371 0.400 0.429 0.437 0.486 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 345 373 384 400 402 408 417 422 472 480 643 693 732 749 750 791 891 369.0 378.5 392.0 401.0 405.0 412.5 419.5 447.0 476.0 561.5 668.0 712.5 740.5 749.5 770.5 841.0 0.543 0.571 0.600 0.629 0.657 0.686 0.714 0.743 0.771 0.800 0.829 0.857 0.886 0.914 0.943 0.971 18 325 335.0 0.514 Slide No. 17 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example (cont’d): Halfway House ½ way point ½ way point (52+76)/2=64 (52+76)/2=64 etc. etc. n: total points n: total points (n=35 here) (n=35 here) m: typical point m: typical point (303+313)/2=308 (303+313)/2=308 Obs. No. Cost xm Cumulative Probability Obs. No. Cost xm Cumulative Probability 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 52 76 100 136 137 186 196 205 250 257 264 280 282 283 303 313 317 64.0 88.0 118.0 136.5 161.5 191.0 200.5 227.5 253.5 260.5 272.0 281.0 282.5 293.0 308.0 315.0 321.0 0.029 0.057 0.086 0.114 0.143 0.171 0.200 0.229 0.257 0.286 0.314 0.343 0.371 0.400 0.429 0.437 0.486 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 345 373 384 400 402 408 417 422 472 480 643 693 732 749 750 791 891 369.0 378.5 392.0 401.0 405.0 412.5 419.5 447.0 476.0 561.5 668.0 712.5 740.5 749.5 770.5 841.0 0.543 0.571 0.600 0.629 0.657 0.686 0.714 0.743 0.771 0.800 0.829 0.857 0.886 0.914 0.943 0.971 18 325 335.0 0.514 9 Slide No. 18 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example (cont’d): Halfway House The value for xm is the mth one. ∴ it should have cumulative probability of m/n. Example: P(C ≤ 64) =1/35 ≅ 0.029 Example: P(C ≤ 64) =1/35 ≅ 0.029 P(C ≤ 308) =15/35 ≅ 0.429 P(C ≤ 308) =15/35 ≅ 0.429 P(C ≤ 335) =18/35 ≅ 0.514 P(C ≤ 335) =18/35 ≅ 0.514 Do for all 35 points and then smoothly extrapolate for the tails Do for all 35 points and then smoothly extrapolate for the tails Slide No. 19 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example (cont’d): Halfway House extrapolated Cumulative Probability 1.00 0.75 can automate easily 0.50 (e.g. RiskView) (e.g. RiskView) 0.25 Yearly Bed-Rental Cost 0.00 0 100 200 300 240 400 450 500 600 700 800 900 extrapolated We can say that there is: We can say that there is: - 50% chance that the yearly bed-rental cost will fall between $240 and $450. - 50% chance that the yearly bed-rental cost will fall between $240 and $450. - 25% chance that the cost would fall below $240. - 25% chance that the cost would fall below $240. - 25% chance that it would fall above $450. - 25% chance that it would fall above $450. 10 Slide No. 20 CHAPTER 10. USING DATA ENCE 627 ©Assakkaf Using Data to Construct Probability Distributions: Empirical CDFs Example (cont’d): Halfway House – Alternatively, could use a discrete approximation e.g. three-point PearsonTukey method 0.05frac...
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This note was uploaded on 10/24/2012 for the course ESI 6385 taught by Professor Mansoorehmollaghasemi during the Fall '12 term at University of Central Florida.

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