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 pays a premium to
the insurer
In return the insurer r
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
; so that
The
random variable is a transformation of X
w
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 joint
distribution
Discrete:
Continuous:
Expectation
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
Standard
normal distribution is
Fun things to do with
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 periods of time
Ex: If represents the number of custo
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 random
variable
If
n is a positive integer
The n-th
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
integers
Ex: coin flips, dice rolls, etc
X
is described by
Section 03
Combinatorial Principles,
Permutations, and
Combinations
Permutations vs.
Combinations
Permutations
are ordered
Combinations are not ordered
Therefore, there are more permutations
than combinations for given and
Both
apply to combinatorics
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 Total Probability
This
is a manipulation of the 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 of this HW page and correct the false ones:
a. Students
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
Stan Dev
3.0
SD/Mean
0.30
Coef of variation
PMF: N(k + .5)
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 Value of the PV of the Payment
Example: If you will ge
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 possible
integers from 1 to 6).
Probability Function (PF):