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CIVL 181 Tutorial 5

CIVL 181 Tutorial 5. Return period Poisson process Multiple random variables. A question on return period. If P (exceedence within the life time of the building, i.e., 10 years) = 0.1. Return period T = 100 years?. Poisson process. 1. The r.v. is continuous or discrete?

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CIVL 181 Tutorial 5

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  1. CIVL 181 Tutorial 5 Return period Poisson process Multiple random variables

  2. A question on return period If P (exceedence within the life time of the building, i.e., 10 years) = 0.1 Return period T = 100 years?

  3. Poisson process 1. The r.v. is continuous or discrete? 2. What is the relation between Poisson and binomial? 3. v / vt?

  4. Comparison of two families of occurrence models

  5. Joint and marginal PDF of continuous R.V.s marginal PDF fX (x) marginal PDF fY (y) x=a fX (a) = Area fX,Y (x, y=b) Surface = fX,Y (x,y) y =b Joint PDF fY (b) = Area Conditional PDF of Y given x=a fY|X(y|x =a) fX,Y (x=a, y)

  6. a) Calculate probability

  7. b) Derive marginal distribution

  8. c) Conditional distribution

  9. Example: Bivariate normal distribution (3.55) A formal def of bivariate normal distribution is: also by arithmetic we can rewrite as Find P(4 <Y< 6) if fX(x) is N (3,1), fY(y) is N (4,2) = 0.2 when x = 3, 3.5, 4

  10. Take x = 3.5 as example Compare to (Double integral!)

  11. (Take x = 3.5 as example)

  12. (Take x = 3.5 as example,) Knowing fY|X(y|x) = N (4.2, 1.95) P(X = 3.5, 4 <Y< 6) = 0.361 Try X = 4, X = 3 as exercise 4.2 1.95

  13. Ex 3.58 The daily water levels (normalized to respective full condition) of 2 reservoirs A and B are denoted by two r.v. X and Y have the following joint PDF:

  14. (a) Determine the marginal density function of daily water level for reservoir A

  15. (b) If reservoir A is half full on a given day, what is the chance that water level will be more than half full?

  16. (c) Is there any statistical correlation between the water levels in the two reservoirs?

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