hw1 soln

hw1 soln - Dr. Behnaam Aazhang ELEC 430 Department of...

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Unformatted text preview: Dr. Behnaam Aazhang ELEC 430 Department of Electrical and Computer Engineering Rice University Due 17 Jan 2008 HOMEWORK 1 Probability Exercise 1. Change of Variables The current I in a semiconductor diode is related to the voltage V by the relation I = e V- 1. If V is a random variable with density function f V ( x ) = 1 2 e-| x | for- < x < , find f I ( y ); the density function of I . Exercise 2. Axioms of Probability (a) Show that if A B = { } then P [ A ] P B C (b) Show that for any A,B,C we have P [ A B C ] = P [ A ] + P [ B ] + P [ C ]- P [ A B ]- P [ A C ]- P [ B C ] + P [ A B C ] (c) Show that if A and B are independent then P A B C = P [ A ] P B C which means that A and B C are also independent. Exercise 3. Probability Distributions Suppose X is a discrete random variable taking on values { , 1 , 2 ,...,n } with the following probability mass function: p X ( k ) = n !...
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hw1 soln - Dr. Behnaam Aazhang ELEC 430 Department of...

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