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Homework #4
Due Monday, 10/1 at start of class
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) = 2/27
P(X=1) = 6/27
P(X=2) = ?
P(X=3) = 9/27
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 four sides are labeled 1, 3, 5, and 10
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.
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.
Thus getting a “5” is 10 times as likely as getting a “1”, the probability of a
“4” is four times the probability of a “2”, etc.
a)
Find the Probability Mass Function P
X
(x).
b)
Find P(X
≤
5)
c)
P(X
≠
4  3 < X
≤
5)
d) Find the probability of rolling a number greater than or equal to “4” three times in a
row.
e)
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This homework help was uploaded on 02/26/2008 for the course IE 111 taught by Professor Storer during the Spring '07 term at Lehigh University .
 Spring '07
 Storer

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