Section 10
Review of Risk
Management Concepts
Loss distributions and
insurance
An
insurance policy is a contract
between the party that is at risk (the
policyholder) and the insurer
The policyholder
Section 09
Functions and
Transformations of
Random Variables
Transformation of
continuous X
Suppose
X is a continuous random variable
with pdf and cdf
Suppose is a one-to-one function with inverse
;
Section 08
Joint, Marginal, and
Conditional
Distributions
Joint distribution of X
and Y
defined over a two-dimensional region
Discrete:
Continuous:
X
and Y may be independent or dependent
CDF of a
Section 07
Continuous
Distributions
Uniform
x
has equal probability over entire
interval
Parameters:
a beginning of interval
b end of interval
Normal
Parameters:
mean
2 variance
n sample size
Section 06
Discrete Distributions
Uniform
x is one specific
Parameters:
outcome
N number of points
Poisson
x
is the number of events in a period of time
Parameters:
Lambda
can be manipulated for
Section 05
Expectation and other
distribution
parameters
Expected value
The
expected value, or expectation, is
the average or mean of the random
variable
Denoted
Discrete:
Continuous:
Moments of a
Section 04
Random Variables and
Probability
Distributions
Discrete random
variables
X
has a discrete distribution if it
takes on values only from a finite or
countable infinite sequence usually
integ
Section 03
Combinatorial Principles,
Permutations, and
Combinations
Permutations vs.
Combinations
Permutations
are ordered
Combinations are not ordered
Therefore, there are more permutations
than c
Section 02
Conditional Probability
and Independence
Conditional Probability
Conditional probability of event B given
event A:
This can be rewritten as and is known as
the multiplication rule
Law of
RM 297C HW #1
Last Name Evans
First Andrea
1. Read my syllabus and bring to class. It is in ANGELs Lessons tab. Refer to it for the following True/False
questions. Hand write answers on the left side
BINOMIAL; NORMAL APPROXIMATION; MONTE CARLO FORECASTING 9/4/2015
Pr Die
Pr Live
10%
90%
=q
=p
Binomial K =
Binomial CDF
Binomial PMF
By Formula
Label variables in Name Box
N
100
Mean
10
Variance
9
Sta
Chapter 6: Models in Life Contingencies (MLC Exam)
6-1: Fair Price = Expected Value
Life Insurance
Fair Price = Payment Amount x PV factor x Probability of getting
that payment
This is the Expected
Chapter 2 Probability
Discrete Uniform Distribution: The probability is the same at each possible value and is
discrete because there are only a finite number of possible values (i.e., a die with poss