HOMEWORK 1, ACTS 4306
What is the derivative of 2x2 (5x4 + 3)?
2
What is the derivative of 3xe4x +3 ?
2 +5
2x
What is the derivative of sin(x2 ) ?
Find the limit of
2x/2 2
2x 4
as x 2.
5. Consider a function f (x, y) = x2y for x, y > 0. Find partial deriv
Course Syllabus
Course Information
STAT 4351.501 Monday and Wednesday, 7 8:15 PM, GR 2.302
Call Number: 84333
Course Title: Probability
Term: Fall 2016
Professor Contact Information
(Professors name, phone number, email, office location, office hours, oth
Fundamentals and conditional probabilities
P[Ac ] = 1 P[A]
P[A | B] =
P[A B] = P[A] + P[B] P[AB]
P[AB]
P[B]
P[AB] = P[B]P[A | B]
A and B are mutually exclusive if P[AB] = 0.
A and B are independent if P[AB] = P[A]P[B], which also implies that P[A | B] = P
Christians Study Notes for Exam P
Kind of like Cliffs Notes, except these are Christians notes.
Complements
C
Either A occurs, or it does NOT occur: ! Pr( A ) = 1 Pr( A).
Unions
! Pr( A B ) = Pr( A) + Pr( B ) Pr( A B ).
You also must the know the extensio
1/P Sample Exam 6
1. Chris has four independent nancial risks. He purchases separate insurance policies to cover the risks,
each with a deductible of 20. What is the probability that Chris will receive a payment from his insurers
given that he has a loss
1/P Sample Exam 7
1. Let X be a Poisson random variable with second moment 6. Find P[X = 3].
A. 0.06
B. 0.12
C. 0.18
D. 0.20
E. 0.22
2. Let X and Y have joint probability density function
f (x, y) =
3
2
32 (x
+ y2)
0
0 < x < 2,
otherwise.
0<y<2
Find the e
1/P Sample Exam 5
1. Losses L have a continuous uniform distribution on (0, 5). What is the probability that L2 < 4L 3?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6
2. Weekly losses last year had a normal distribution with mean 100 and variance 400. Let X denote th
1/P Sample Exam 6
1. Chris has four independent nancial risks. He purchases separate insurance policies to cover the risks,
each with a deductible of 20. What is the probability that Chris will receive a payment from his insurers
given that he has a loss
1/P Sample Exam 7
1. Let X be a Poisson random variable with second moment 6. Find P[X = 3].
A. 0.06
B. 0.12
C. 0.18
D. 0.20
E. 0.22
2. Let X and Y have joint probability density function
f (x, y) =
3
2
32 (x
0
+ y 2) 0 < x < 2,
0<y<2
otherwise.
Find the
1/P Sample Exam 5
1. Losses L have a continuous uniform distribution on (0, 5). What is the probability that L2 < 4L 3?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
E. 0.6
2. Weekly losses last year had a normal distribution with mean 100 and variance 400. Let X denote th
SOCIETY OF ACTUARIES
EXAM P PROBABILITY
EXAM P SAMPLE SOLUTIONS
Copyright 2015 by the Society of Actuaries
Some of the questions in this study note are taken from past examinations.
Some of the questions have been reformatted from previous versions of thi
STAT 4351: Homework 2
Due by September 12, 2016
Yuly Koshevnik
Problem 1
A die has N faces numbered as cfw_i = 1, 2, . . . , N . A probability that the die shows i is the same, for all i
values. The die is rolled N times (assume that rolls are independent
STAT 4351: Homework 3
Due by September 28, 2016
Yuly Koshevnik
Problem 1: 10 points
A random variable (Y ) has the Poisson distribution with intensity > 0, that is:
P [Y = k] =
k
e for k = 0, 1, 2, . . . .
k!
A new variable (Z) is defined as Z = 2Y .
1.
HOMEWORK 2, STAT 4351
All problems are from the text, pp. 3039
1. Exerc. 2.4(c)
2. Exerc. 2.5(b)
3. Exerc. 2.6
4. Exerc. 2.7
5. Exerc. 2.8
6. Exerc. 2.9(a)
7. Exerc. 2.9(b)
8. Exerc. 2.11
9. Exerc. 2.14
10.Exerc. 2.15
Very nice extra problem (no points):
HOMEWORK 3, ACTS 4306
For each problem, you need to choose a correct answer among 5 given answers. Note that
during exam you have 60 minutes to solve 10 problems, so keeping track of time is useful.
Another remark: you need to solve correctly (about) 7 pr
HOMEWORK 2, ACTS 4306
For each problem, you need to choose a correct answer among 5 given answers. Note that
during exam you have 60 minutes to solve 10 problems, so keeping track of time is useful.
Another remark: you need to solve correctly (about) 7 pr
SOLUTION FOR HOMEWORK 1, ACTS 4306
Welcome to your rst homework. It is devoted to some topics in calculus that you must
know very well. If not dust o books and review the stu. I am not going to discuss it
in class.
All my solutions for a homework may cont
SOLUTION FOR HOMEWORK 2, ACTS 4306
Welcome to your second homework. It is devoted to the algebra of events. All problems
from former SOA exams.
All my solutions for a homework may contain some seeded mistakes. As a result, it is
prudent to do all problems
SOLUTION FOR HOMEWORK 3, STAT 4351
Welcome to your third homework which rounds out topics in Chapter 2. Now you know
basics of Probability, Kolmogorovs axioms, basics of algebra of sets, conditional probability,
independence/dependence of events, notion o
SOLUTION FOR HOMEWORK 2, STAT 4351
Well, welcome to your second homework. Here we will be trained in dealing with abstract
events, their algebra and probabilities. It takes some time to get used to the technique, but
eventually you will like it.
Now let u
SOLUTION FOR HOMEWORK 1, STAT 4351
Well, welcome to your rst homework. First of all, I would like to chat with you a bit
about Combinatorial Methods (Chapter 1).
Combinatorics is a very sophisticated part of mathematics, and in the class we just touch
it.
SOLUTION FOR HOMEWORK 3, ACTS 4306
Welcome to your third homework.
For the suggested problems it is very important to choose a meaningful and short notation
so you can visualize everything simpler. See how I did it in all solutions.
1. Notation: C - Colli
STAT 4351: Homework 1
Answers and Solutions
Due by August 31, 2016
Yuly Koshevnik
Problem 1
A balanced coin is tossed until a head appears.
(A) Find the probability that the head will not appear on the first 5 flips.
(B) Find the probability that the coin
STAT 4351: Homework 2
Answers and Solutions
Due by September 12, 2016
Yuly Koshevnik
Problem 1
A die has N faces numbered as cfw_i = 1, 2, . . . , N . A probability that the die shows i is the same, for all i
values. The die is rolled N times (assume that
STAT 4351: Homework 1
Due by August 31, 2016
Yuly Koshevnik
Problem 1
A balanced coin is tossed until a head appears.
(A) Find the probability that the head will not appear on the first 5 flips.
(B) Find the probability that the coin will be tossed at lea
STAT 4351: Exam 1 Solutions
September 19, 2016
Yuly Koshevnik
Problem 1: 10 points
A probability function, p (k) = P [Y = k] , of a discrete random variable Y satisfies the identity:
p (k + 1) =
1. Show that p (k) = C
k
1
3
1
p (k) , for all (k = 0, 1,