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Practice Problems for Probability Quiz - Random Processes | ECE 534, Quizzes of Electrical and Electronics Engineering

University of Illinois - Urbana-ChampaignElectrical and Electronics Engineering
Prof. Rayadurgam Srikant

Material Type: Quiz; Professor: Srikant; Class: Random Processes; Subject: Electrical and Computer Engr; University: University of Illinois - Urbana-Champaign; Term: Fall 1999;

Typology: Quizzes

Pre 2010

Uploaded on 02/24/2010

koofers-user-h8d
koofers-user-h8d 🇺🇸

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ECE 434 -- RANDOM PROCESSES FALL 1999
Probability Quiz Tuesday,
Sept. 14
You have 60 minutes to complete the exam. The exam will be closed book and closed
note.
You must show your work for full credit.
There are three problems on three pages, for a total of 25 points.
1. (9 points) Let U and V be independent random variables, each uniformly distributed on
the interval [0,1].
(a) What is the variance of U2?
(b) What is the variance of U2+2V+1?
(c) Suppose two marks are placed on a stick of length one. One mark is distance U from
one end and the other mark is distance V from the same end. If the stick is cut at both
marks, what is the probability that the resulting three sticks can be used to form a
triangle?
pf3

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Download Practice Problems for Probability Quiz - Random Processes | ECE 534 and more Quizzes Electrical and Electronics Engineering in PDF only on Docsity!

ECE 434 -- RANDOM PROCESSES FALL 1999

Probability Quiz Tuesday,

Sept. 14

You have 60 minutes to complete the exam. The exam will be closed book and closed note. You must show your work for full credit. There are three problems on three pages, for a total of 25 points.

  1. (9 points) Let U and V be independent random variables, each uniformly distributed on the interval [0,1]. (a) What is the variance of U^2? (b) What is the variance of U^2 +2V+1? (c) Suppose two marks are placed on a stick of length one. One mark is distance U from one end and the other mark is distance V from the same end. If the stick is cut at both marks, what is the probability that the resulting three sticks can be used to form a triangle?
  1. (8 points) Let X be exponentially distributed with mean one, and let Y=2-÷X. Find and carefully sketch the probability density function fX and cumulative distribution function FX of X. Label the axes.