University of Illinois
Fall 2009
ECE 313:
Problem Set 8
Independent Events; System Reliability; CDFs
Due:
Wednesday October 21 at 4 p.m.
Reading:
Ross, Chapter 3.4, 3.5, and 4.10; Powerpoint Lecture Slides, Sets 18-21
Noncredit Exercises:
Chapter 3:
Problems 53, 58, 59, 62, 63, 70-74, 78, 81
Theoretical Exercises 6, 7(a), 25, 26; Self-Test Problems 15-26.
1.
[“I before E except after C”]
Let
A
and
B
denote two
mutually exclusive
events that can occur on a trial of an experiment. Repeated
independent trials of the experiment are carried out until either the event
A
or the event
B
occurs.
What is the probability that
A
occurs before
B
does?
2.
[What happens in Vegas stays in Vegas]
The dice game of
craps
begins with the player (called the
shooter
) rolling two fair dice. This is called
the
ﬁrst roll
. If the sum is 2, 3, or 12, the shooter loses the game. If the sum is a 7 or 11, the shooter
wins the game. If the sum is any of 4, 5, 6, 8, 9, 10, then the shooter has neither won nor lost (as yet).
The number rolled is called the shooter’s
point
, and what happens next is described in parts (b) and
(c) below.
(a) What is the probability that the shooter wins the game on the ﬁrst roll? What is the probability
that the shooter loses the game on the ﬁrst roll? What is the probability that the shooter’s point
is
i,i
∈ {
4
,
5
,
6
,
8
,
9
,
10
}
? We need 6 answers here for this last part, folks!
(b) Suppose that the shooter’s point is