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EE 351K Probability, Statistics, and Random Processes
SPRING 2009
Instructor: Shakkottai/Vishwanath
{
shakkott,sriram
}
@ece.utexas.edu
Homework 3
Due Wednesday, February 18th 2009
Problem 1
You are visiting the rainforest, but unfortunately your insect repellent has run out. As
a result, at each second, a mosquito lands on your neck with probability 0.5. If a mosquito lands, it will
bite you with probability 0.3, and it will never bother you with probability 0.7, independently of other
mosquitoes. What is the expected time between successive bites?
Problem 2
Let
X
1
,...,X
n
be independent, identically distributed random variables with common
mean and variance. Find the values of
c
and
d
that will make the following formula true:
E
[(
X
1
+
....
+
X
n
)
2
] =
c
(
E
[
X
1
])
2
+
dE
[(
X
1
)
2
]
.
Problem 3
A class of
n
students takes a test in which each student gets an A with probability
p
, a B
with probability
q
, and a grade below B with probability
1

p

q
, independently of any other student. If
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This note was uploaded on 10/26/2009 for the course EE 351k taught by Professor Bard during the Spring '07 term at University of Texas at Austin.
 Spring '07
 BARD

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