Mathematics Department, UCLA
P. Caputo
Fall 08, midterm 2
Nov 19, 2008
Midterm 2: Math 170A Probability, Sec. 2
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(if you are an extension student, say so)
Please note:
1. Provide the information asked above and write your name on the top of each page.
2. The only thing you may use during the exam is a pen to write down your answers. Every
thing else (calculator, textbook, notes, your own paper, . . . ) has to be put away safely.
3. Cheating in any way will not be tolerated. Do not speak during the exam.
4. Show your work and explain what you are doing. This is more important than just finding
the right answer.
5. You can use the blank pages as scratch paper or if you need more space to finish the
solution to a question. When you continue on another page indicate this clearly.
6. The maximal number of points attainable is given at the beginning of each question.
Good Luck!
Question
1
2
3
4
5
Total
Score
out of
10
10
10
10
10
50
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Name:
1.
(10 pts)
Consider independent rolls of a fair die. Let
X
denote the number of rolls needed
to see the first even face and let
Y
denote the number of rolls needed to see the first face
larger than 3. Find:
a).
E
[
X
] and
E
[
Y
].
b).
P
(
X >
2

Y
= 2).
c).
P
(
X
=
Y
)
Solution
.
a)
X
and
Y
are both geometric random variables with parameter
p
=
1
2
. Therefore
E
[
X
] =
E
[
Y
] =
1
p
= 2
.
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 Fall '08
 staff
 Probability, Variance, Probability theory, exponential random variable, random variable zt

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