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Lec_wk8_1&2

# For example in matlab common lognrnd generates random

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Unformatted text preview: enerates random numbers following lognormal distribution and the two input parameters used to characterize the distribution are expectation and standard deviation of the corresponding normal distribution. Also, when dealing with samples/observations from a random variable following lognormal distribution, geometric mean and geometric standard deviation are commonly given: g ( X ) exp( ) g ( X ) exp( ) It can be shown that the geometric mean of a lognormal distribution is its median, and is smaller than its actual mean (or arithmetic mean). Note: Geometric mean of a data series: Geometric standard deviation: 3 Two random variables: joint CDF joint CDF ∬ ( ) )( )] Independence: X and Y are independent if and only { Expectation: [ =∫ [ Covariance: ∫ [{ [ [ If [ [ But uncorrelated [ independent! Dependence does not mean correlation. Random Vector: [ Covariance Matrix: [ [ ∑[ [ 4 [ Monte-Carlo Simulation Repeated random sampling to capture effects due to uncertainties in inputs. key point is random number generation. Require (joint) probability distributions, however, this may be difficult to get in reality. In LCA, independence is usually assumed, but mass/energy conservation has to be applied as constrains. Other known equations may also be applied. Uniform, Lognormal, and triangular distributions are most commonly used. Ma...
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