Exercise 12 p.248
Statement:
A bus travels between the two cities A and B , which are 100 miles apart. If the bus has a breakdown, the distance
from the breakdown to city A has a uniform distribution
Chapter 1: Combinatorial Analysis
The mathematical theory of counting is formally known as combinatorial analysis.
Basic Principle of Counting
Suppose that two experiments are to be performed. Then if
Chapter 3: Conditional Probability and Independence
Section 1: Introduction
Conditional probability is a concept used in
1. calculating probabilities when some partial information concerning the resul
Chapter 2: Axioms of Probability
Section 2: Sample Space and Events
For a given experiment, the set of all possible outcomes is called the sample space of the experiment and is
denoted by S . Any subs
Chapter 8: Limit Theorems
Section 1: Introduction
The most important theoretical results in probability theory are the limit theorems. Of these theorems, the ones of
most value are either laws of larg
Chapter 4: Random Variables
Section 1: Random Variables
Definition: If S is a sample space for an experiment, then a random variable X is a real-valued function of S ,
i.e., X : S 6 R .
If X is a rand
Chapter 7: Properties of Expectation
Section 1: Introduction
Definition: If X is a discrete random variable with probability mass function p(x) , then the expectation or the
expected value of X , deno
Chapter 5: Continuous Random Variables
Section 1: Introduction
Definition: X is called a continuous random variable if there exists a non-negative function f , defined for all real
x ( -4, 4 ) , havin
Chapter 6: Jointly Distributed Random Variables
Section 1: Joint Distribution Functions
Definition: For any two random variables X and Y , the joint cumulative distribution function of X and Y is
defi
Math 230 Worksheet #4
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SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY
EXAM P PROBABILITY
EXAM P SAMPLE SOLUTIONS
Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society
Some of the questions in this s
Exercise 15, Page 115
Statement:
One probability class of 30 students contains 15 that are good, 10 that are fair, and 5 that are of poor quality. A
second probability class, also of 30 students, cont
Solution to Exercise #14 on p.188
Statement of Exercise :
Five distinct numbers are randomly distributed to players numbered 1 through 5. Whenever two players
compare their numbers, the one with the h
An Example of Mathmatical Finance
This example is to illustrate the amount of knowledge necessary to address a relatively straightforward
application of probability in the eld of mathematical nance.
E
Exercise 41 p.251
Statement :
Find the distribution of R D A sin. /, where A is a xed constant and
is uniformly distributed on .
=2; =2/.
Solution:
There are two methods for determining the distributi
Some Exercises from Chapter 1
Statements of the Exercises
1. Twenty workers are to be assigned to 20 dierent jobs, one to each job. How many dierent
assignments are possible?
2. John, Jim, Jay, and Ja
Chapter 4 Example 4b, p.129
Statement:
A product that is sold seasonally yields a net prot of b dollars for each unit sold and a net loss of l dollars for
each unit left unsold when the season ends. T
Solution to Exercise #23 on p.190
Statement:
You have $1000 and a certain commodity presently sells for $2 per ounce. Suppose that after one week the
dommodity will sell for either $1 or $4 per ounce,
Some Exercises from Chapter 2 Exercise 5(c)
In this part of the problem, the sample space S consists of ordered pairs of students. Thus all events consists of
such pairs.
Let S t 1 be the event that t
Exercises from Chapter 4
Statements of the Exercises
1. Two fair dice are rolled. Let X equal the product of the 2 dice. Compute P (X = i) for i = 1, 2, . . .
2. Five men and ve women are ranked accor
Some Exercises from Chapter 3
Statements of the Exercises
1. If two fair dice are rolled, what is the conditional probability that the rst one lands on 6 given
that the sum of the dice is i? Compare a
Some Exercises From Chapter 5
Statements of the Exercises
1. A system consists of one original unit plus one spare can function for a random amount of time
X . If the density of X is given (in units o