Virginia Tech
The Bradley Department of Electrical and Computer Engineering
ECE 5605 – Stochastic Signals and Systems – Fall 08
Problem Set 1
Problem 1.
A random experiment has sample space
S
=
{
a,b,c
}
. Suppose that
P
[
{
a,c
}
] = 5
/
8
and
P
[
{
b,c
}
] = 7
/
8. Use the axioms of probability to ﬁnd the probabilities of the elementary
events.
Problem 2.
Computer programs are classiﬁed by the length of the source code and by the
execution time. Programs with more than 150 lines in the source code are big (
B
). Programs
with
≤
150 lines are little (
L
). Fast programs (
F
) run in less than 0.1 seconds. Slow programs
(
W
) require at least 0.1 seconds. Monitor a program executed by a computer. Observe the
length of the source code and the run time. The probability model for this experiment contains
the following information:
P
[
LF
] = 0
.
5,
P
[
BF
] = 0
.
2, and
P
[
BW
] = 0
.
2. What is the sample
space of the experiment? Calculate the following probabilities:
(a) Probability that a program is slow.
(b) Probability that a program is big.
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 Fall '08
 DASILVER
 Probability, Probability theory

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