This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 !...
View
Full Document
 Spring '08
 Aazhang
 Volt, Probability theory, Probability mass function, Gaussian random variables, Proakis, Probability exercise

Click to edit the document details