IE 111 Fall Semester 2011
Homework #4
Due Wednesday 10/5
Question 1.
Suppose we have a biased coin such that P(head)
≠
P(tail).
Suppose I flip the coin three
times.
Let the random variable X be the number of heads in the 3 flips.
You are given
the following information:
P(X=0) = 0.343
P(X=1) = 0.441
P(X=2) = ?
P(X=3) = 0.027
a)
Find P(X=2)
b)
Find P(X
≤
1)
c)
Find P( 1
≤
X < 2)
d)
Find P( X=1  X
≤
1)
Question 2.
A die has 4 sides (not 6 like a regular die).
The five sides are labeled 1, 3, 5, 10, and 20
respectively.
It is equally likely that you will get a 1 or a 3.
It is equally likely that you
will get a 5 or a 10.
It is three times more likely that you will get a 5 or10 than a 1 or 3. It
is two times as likely that you will get a 20 than a 1 or 3
a)
Let X = the outcome of a roll of the die.
Find the probability mass function of X.
b)
If Y=2X
2
+1,
find P
Y
(y)
c)
If I roll the die 10 times, what is the probability I get exactly 3 tens?
Question 3.
Let the random variable X be the value of the up face of a certain
unfair
die.
For this die,
the probability of getting a specific number (1 through 6) is proportional to twice that
number.
a)
Find the Probability Mass Function P
X
(x).
b)
Find P(X
≥
2)
c)
P(X
≠
4  3 < X
≤
5)
d)
Find the probability of rolling a number greater than or equal to “3” four times in
a row.
e)
The Cumulative Distribution Function F
X
(x)
is Defined as F
X
(x)
= P(X
≤
x)
Find the C.D.F. for the random variable X.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Question 4.
The cumulative distribution function F
X
(x) of a random variable X is given by:
F
X
(x) = 0
for x < 5
F
X
(x) = 0.6
for 5
≤
x < 6
F
X
(x) = 0.8
for 6
≤
x < 10
F
X
(x) = 1.0
for
x
≥
10
a)
Find the probability mass function P
X
(x).
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 Storer
 Probability theory, Cumulative distribution function, Probability mass function

Click to edit the document details