Probability Theory, Math 170a, Fall 2012, Toni Antunovi c
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Homework 1
From the textbook solve the problems 2 (parts b and c), 10, 54, 56 at the
end of the Chapter 1.
Solve the problems 1, 2, 3, 5, 36 from the Chapter 1 additional exercises at
http:/www.a
Probability Theory, Math 170a, Fall 2012, Toni Antunovi c
c
Homework 1
From the textbook solve the problems 2 (parts b and c), 10, 54, 56 at the
end of the Chapter 1.
Solve the problems 1, 2, 3, 5, 36 from the Chapter 1 additional exercises at
http:/www.a
Probability Theory, Math 170a, Fall 2012, Toni Antunovi c
c
Homework 2
From the textbook solve the problems 14, 16, and 19 at the end of the
Chapter 1.
Solve the problems 15, 16, 18, 31, from the Chapter 1 additional exercises
at
http:/www.athenasc.com/pr
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 6
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From the textbook solve the problems 32, 39, 40 at the end of the Chapter 2.
Solve the problems 16, 17, 18, 20, 21 from the Chapter 2 additional exercises at
http:/www.athenasc.com/p
Probability Theory, Math 170a, Fall 2012, Toni Antunovi c
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Homework 3
From the textbook solve the problems 30, 33, 34, 35 and 36 at the end of
the Chapter 1.
Solve the problems 24, 25, 28 and 30 from the Chapter 1 additional exercises
at
http:/www.athena
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 5
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From the textbook solve the problems 16, 22, 24 at the end of the Chapter 2.
Solution to Problem 16:
(a) To nd a use the condition that the probabilities must add up to 1:
pX (3) + p
Midterm 1, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Printed name:
Signed name:
Student ID number:
Instructions:
Read problems very carefully. If you have any questions raise your hand.
The correct nal answer alone is not sucient for fu
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 5
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From the textbook solve the problems 16, 22, 24 at the end of the Chapter 2.
Solve the problems 5 and 13 from the Chapter 2 additional exercises at
http:/www.athenasc.com/prob-supp.h
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 2
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solutions
From the textbook solve the problems 14, 16, and 19 at the end of the Chapter 1.
Solution to Problem 14:
a) There are 6 possible outcomes for doubles, for the probability i
Probability Theory, Math 170a, Fall 2012, Toni Antunovi c
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Homework 3
From the textbook solve the problems 30, 33, 34, 35 and 36 at the end of
the Chapter 1.
Solution to Problem 30: In the rst case the hunter could choose the
correct path either if both
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 6
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From the textbook solve the problems 32, 39, 40 at the end of the Chapter 2.
Solution to Problem 32: Let Xi be the indicator of the event that the rst person in the
i-th couple is al
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 4
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solutions
From the textbook solve the problems 3, 4, 5, 9, and 10 at the end of the Chapter 2.
Solution to Problem 3:
a) The probability that Fischer wins the match in the 1st game i
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 4
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From the textbook solve the problems 3, 4, 5, 9, and 10 at the end of the Chapter 2.
Solve the problem 4 from the Chapter 2 additional exercises at
http:/www.athenasc.com/prob-supp.h
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Homework 7
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Problem 1. We have a biased coin (probability of heads equal to p). In the rst stage of the
experiment we keep tossing it until we get a heads, and we remember how many times we had
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Lecture 1
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We start the course by giving a rigorous mathematical denition of the notion of probability
(more precisely we will talk about Probabilistic Models and Probability Laws). The denition
Probability Theory, Math 170a, Fall 2012, Toni Antunovi - Lecture 2
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Sets
Before talking about this properties in the denition of the probability law, we will talk a bit
about sets. To connect this to above story, keep in mind an experiment of choosing
Midterm 1 practice, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Name and student ID:
Question
Points
1
12
2
10
3
10
4
10
5
8
Total:
50
Score
1. (a) (6 points) If = A B , P(A B c ) = 0.6, P(Ac B ) = 0.2 nd the probabilities of A and B .
(b)
Midterm 1 practice, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Name and student ID:
Question
Points
1
12
2
10
3
10
4
10
5
8
Total:
50
Score
1. (a) (6 points) If = A B , P(A B c ) = 0.6, P(Ac B ) = 0.2 nd the probabilities of A and B .
Solu
Midterm 1, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Printed name:
Signed name:
Student ID number:
Instructions:
Read problems very carefully. If you have any questions raise your hand.
The correct nal answer alone is not sucient for fu
Midterm 2 practice, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Name and student ID:
Question
Points
1
10
2
10
3
10
4
10
5
10
Total:
50
Score
1. (a) (2 points) If var(X 2 ) = 3, var(Y 2 ) = 2 and cov(X, Y ) = 1, what is var(X + Y )?
(b) (2
Midterm 2 practice, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Name and student ID:
Question
Points
1
10
2
10
3
10
4
10
5
10
Total:
50
Score
1. (a) (2 points) If var(X ) = 3, var(Y ) = 2 and cov(X, Y ) = 1, what is var(X + Y )?
Solution:
v
Midterm 2 practice, Math 170a - Lec 3, Fall 2012
Instructor: Toni Antunovi
c
c
Name and student ID:
Question
Points
1
10
2
10
3
10
4
10
5
10
Total:
50
Score
1. (a) (2 points) If var(X ) = 3, var(Y ) = 2 and cov(X, Y ) = 1, what is var(X + Y )?
Solution:
v