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Homework 3 Solutions
July 19, 2007
p187 21, 76, 77 p197 6, 7, 10, 27
1. #21 (a)
E
[
X
] should be larger than
E
[
Y
] because whereas the bus
driver is equally likely to be from any of the 4 buses, the student selected
is more likely to come from a bus carrying a large number of students.
(b)
E
[
X
] =
40
148
40 +
33
148
33 +
25
148
25 +
50
148
50 = 39
.
28.
E
[
Y
] =
1
4
(40 + 33 + 25 + 50) = 37.
2. #76 Let
E
R
be the event that the right box is empty and there are
k
matches in the left box. For the event
E
R
to occur, the discovery that
the right box is empty must be made on the (
N
1
+
N
2

k
+ 1)th trial.
Then
P
(
E
R
) is given by
±
N
1
+
N
2

k
N
1
²
1
2
N
1
1
2
N
2

k
*
1
2
. The calculation for
E
L
, the event that the left box is empty and there are
k
matches in the
right box, is calculated similarly.
The total probability is given by
±
N
1
+
N
2

k
N
1
²
1
2
N
1
1
2
N
2

k
1
2
+
±
N
1
+
N
2

k
N
2
²
1
2
N
2
1
2
N
1

k
1
2
.
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This note was uploaded on 11/15/2008 for the course STATS 116 taught by Professor Staff during the Summer '07 term at Stanford.
 Summer '07
 Staff
 Probability

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