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Homework 9
•
Homework must be answered in the order shown here (else please make a note telling the reader
where it is).
•
Staple the homework
•
Write your answers neatly
•
Work must be shown for full credit
•
No late homework accepted under any circumstances
•
Homework must be turned in in lecture the date it is due. Do not give to TA or leave anywhere.
You must email prof. Sanchez if you want to turn it in early for instructions.
1.Let X
1
denote the amount of gasoline stocked in a bulk tank at the beginning of a week, and let X
2
denote the amount sold during the week:
The random variable
Y
=
X
1
−
X
2
represents the amount left over at the end of the week. Find the
mean and variance of Y using the rules of expectations and variance of sums of random variables. Show
work.
f
x
1
,
x
2
( )
=
3
x
1
0
≤
x
2
≤
x
1
≤
1
0
elsewhere
⎧
⎨
⎩
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2.

A particular fast food restaurant is interested in the joint behavior of the random variable X, defined as
the total time between a customer’s arrival at the store and his or her leaving the service window, and Y,
the time that the customer waits in line before reaching the service window. Because X includes the time
a customer waits in line, we must have X
≥
Y. The relative frequency distribution of observed values of X
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This document was uploaded on 03/20/2011.
 Winter '09

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