# MC - Geog 503 Spatial Uncertainty Analysis \$ Monte Carlo...

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Geog 503. Spatial Uncertainty Analysis & \$ % Monte Carlo method Consider the following equation quantifying the dose D of tetrachloroethylene (in mg kg day ) received by an individual as a function of other pertinent variables: D = C × IR × ED BW × AT where C: denotes the chemical concentration (in mg per liter) IR: denotes the ingestion rate of tapwater (in liters per day) ED: denotes the exposure duration (in days) BW: denotes the body weight (in kg) AT: denotes the averaging time (in days) we assume the following distributions (and fixed values) for the various variables: C follows a log-normal distribution, i.e., log( C ) N (1 . 6 , 0 . 3) . IR follows an Exponential distribution with parameter λ = 1 . ED follows a Gaussian distribution, i.e., ED N (13 , 1 2 ) . BW follows a Uniform distribution, i.e., BW U (50 , 100) . AT is fixed at 25,550 days (70 years). Lab assignment #3 (due 10/06) Eun-Hye Enki Yoo 1 of 4

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Geog 503. Spatial Uncertainty Analysis & \$ % Monte Carlo method: parametric case 1. What is a base-case value for dose, assuming mean inputs? For the concentration C, assume that the mean is 5 . 0 mg per liter. 2. Perform Monte Carlo simulation from the respective distributions of the input variables. Use 100 draws from each distribution as your sample size. 3. Evaluate the uncertainty in dose due to the uncertainty of its inputs. Do so by calculating 100 simu- lated dose values using the 4 × 100 simulated values of the four input variables. Present/summarize your dose predictions. In your summary, apart from the distribution of simulated dose, include nu- merical values for the mean, std deviation, interquartile range, minimum and maximum. Assuming a regulatory threshold on dose of 0 . 02 mg kgday
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