ECE 804, Random Signal Analysis
Oct. 6, 2008
OSU, Autumn 2008
Due: Oct. 13, 2008
Problem Set 2
Problem 1
Let
X
1
, . . . , X
n
be a sequence of numbers, where each number takes on the value 0
,
1 or
2 with probability
1
2
,
1
4
and
1
4
respectively.
(a) What is the total number of all possible sequences?
(b) Let us call two sequences ‘identical’ if they contain identical number of zeros, ones
and twos. What is the total number of ‘distinct’ sequences?
(c) What is the probability that a given sequence contains exactly
n
2
zeros?
(d) Let
n
= 3. Calculate P (number of twos = 2

X
1
+
X
2
+
X
3
= 4).
Problem 2
Two players A and B are playing the following game. There is an urn containing 4 red, 3
yellow and 2 white balls. First, player A draws three balls without replacement and wins
the game if the balls she draws have three di±erent colors. Otherwise, she puts the balls
back and B repeats the same with the same condition of winning. They keep going until
there is a winner.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 UYSALBIYIKOGLU
 Conditional Probability, Probability, Probability theory, Dice, Coin flipping

Click to edit the document details