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Unformatted text preview: University of California, San Diego
Department of Electrical and Computer Engineering ECE109  Spring 2004
Midterm Exam  SOLUTIONS
Wednesday, May 5, 2004 6:30pm 7:50pm
Location: HSS 2250
K. Zeger Name Your UCSD ID Number
Signature INSTRUCTIONS
This exam is open book and open notes. No calculators, laptop computers, or other electronic devices
are allowed.
Write your answers in the spaces provided. Show
all your work. If you need extra space, please use the
back of the previous page. Partial credit will be given
only for substantial progress on a problem. Zero
credit will be given for correct answers that lack adequate explanation of how they were obtained. There
is a maximum total of 40 points on this exam. Simplify your answers as much as possible and leave answers as fractions, not was decimal numbers. GRADING
1. 10 points
2. 10 points
3. 10 points
4. 10 points
TOTAL (40 points) ...
1 Problem 1 (10 points) £¡
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and , respectively. A box
contains 2 gold coins and 3 silver coins. One coin is randomly taken from the box and that coin is
tossed times. We learn that the coin came up Heads on exactly one of the tosses, but we don’t
know which toss. Given this observation, what is the probability that the coin chosen was silver?
Give your answer in terms of and .
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event that the chosen coin was silver. Then we want .
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$ #"! © ¥ y p¤ y be a random variable with probability density function
for
. Find the probability that
is positive. y 3
SOLUTION:
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f7¥3¡ Let , and Problem 2 (10 points) Problem 3 (10 points)
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0¥ Let
be a random variable whose cummulative distribution function
below. Find the expected value of . is shown in the ﬁgure F(u) 2/3
1/2 −1 is
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07 Let be a random variable whose cummulative distribution function
below. Find the expected value of . is shown in the ﬁgure F(u) (1/2)(1−u2)
u 0 is
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¤ so the expected value of y The pdf of SOLUTION: The CDF of 1 ...
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This note was uploaded on 04/07/2008 for the course ECE 109 taught by Professor Kennethzeger during the Spring '08 term at UCSD.
 Spring '08
 KennethZeger

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