quiz00_2 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Civil and Environmental Engineering 1.017 Computing and Data Analysis for Environmental Applications Quiz 2 Thursday, November 9, 2000 Please answer any 5 of the following 6 problems (maximum score = 100 points): Problem 1 (20 points) Suppose that a remote sensing signal z (measured in watts/m 2 ) is the sum of two components x and y which represent emissions from two adjacent regions on the ground (i. .e. z = x + y ). The independent discrete random variables x and y can have the following values x = {1 ,2 }, y = { 1 , 2}, depending on land use. The probabilities of these x and y values are: p x (1) = 0.3 p x (2) = 0.7 p y (1) = 0.8 p y (2) = 0.2 a) What are the possible values for z (present as a table)? b) Derive the probability mass function p z ( z ), assuming that x and y are independent (i.e. p XY ( x , y ) = p X ( x ) p Y ( y )). Plot the probability mass function and cumulative distribution of z vs z . c)
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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quiz00_2 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department...

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