lec2 (1)

# lec2 (1) - Functions of Random Variables Logistical and...

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Functions of Random Variables Logistical and Transportation Planning Methods Massachusetts Institute of Technology Fall 2006

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4 Steps: 1. Define the Random Variables 2. Identify the joint sample space 3. Determine the probability law over the sample space 4. Carefully work in the sample space to answer any question of interest
4 Steps: Functions of R.V.s 1. Define the Random Variables 2. Identify the joint sample space 3. Determine the probability law over the sample space 4. Carefully work in the sample space to answer any question of interest 4a. Derive the CDF of the R.V. of interest, working in the original sample space whose probability law you know 4b Take the derivative to obtain the desired PDF

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± 1. R.V.;s X 1 = location of the accident X 2 = location of the ambulance D = response distance = | X 1 -X 2 | ± 2. Joint sample space is unit square in X 1 X 2 plane ± 3. PDF over square is uniform Response Distance of an Ambulance 0 1 ambulance accident
x1 x 2 1 1 0

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x 1 x 2 y x 2 = x 1 -y y x 2 = x 1 + y x 2 > x 1 x 2 < x 1 Event { D<y } 1 1 0
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## This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.

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lec2 (1) - Functions of Random Variables Logistical and...

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