6 chapter8 Random Variate

Distn inverse transform example suppose the data

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Unformatted text preview: ansform] Example: Suppose the data collected for100 brokenwidget repair times are: i Interval (Hours) x Frequency 0.5 Relative Frequency Cumulative Slope, Frequency, c i ai 31 0.31 0.31 0.81 1 0.25 2 0.5 x 1.0 10 0.10 0.41 5.0 3 1.0 x 1.5 25 0.25 0.66 2.0 4 1.5 x 2.0 34 0.34 1.00 1.47 Consider R1 = 0.83: c3 = 0.66 < R1 < c4 = 1.00 X1 = x(4-1) + a4(R1 – c(4-1)) = 1.5 + 1.47(0.83-0.66) = 1.75 8 Discrete Distribution [Inverse-transform] All discrete distributions can be generated via inverse-transform technique Method: numerically, table-lookup procedure, algebraically, or a formula Examples of application: Empirical Discrete uniform Gamma 9 Discrete Distribution [Inverse-transform] Example: Suppose the number of shipments, x, on the loading dock of IHW company is either 0, 1, or 2 Data - Probability distribution: x p(x) F(x) 0 1 2 0.50 0.30 0.20 0.50 0.80 1.00 Method - Given R, the generati...
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