a&j flashcards for soa exam p/cas exam 1
DESCRIPTION
Now you can review your exam material anywhere, including using your iphone!These flashcards have 260 pages covering every topic in the syllabus of the exam. It is written in a way that helps you to remember the materials by listing the steps to solve for some particular questions and by generalizing formulas covered in the exam. As such, not only you are able to remember the material accurately, you are also able to apply the concepts to the exam questions more effectively.TRANSCRIPT
A&J Flashcards for
Exam P/1 1st Edition
Alvin Soh
Outline
A&J © 2010. These flashcards were purchased by [Candidate P].
A) Combinatorial Analysis
B) Basic Probability and Set Theory
C) Conditional Probability and Bayes Formula
D) Discrete Random Variables
E) Discrete Probability Distribution
F) Continuous Random Variables
G) Continuous Probability Distribution
H) Jointly Distributed Random Variables with its Applications
I) Jensen Inequality and Chebyshev’s Inequality
J) Application of Probability in Risk Management
Basic Probabilities and Set Theory
A&J © 2010. These flashcards were purchased by [Candidate P].
Distributive Law
Basic Probabilities and Set Theory
A&J © 2010. These flashcards were purchased by [Candidate P].
A B C AC BC
AB C AC BC
Basic Probabilities and Set Theory
A&J © 2010. These flashcards were purchased by [Candidate P].
De Morgan’s Law
Basic Probabilities and Set Theory
A&J © 2010. These flashcards were purchased by [Candidate P].
1 1
Cn n
C
i i
i i
E E
1 1
Cn n
C
i i
i i
E E
Basic Probabilities and Set Theory
A&J © 2010. These flashcards were purchased by [Candidate P].
Law of Total Probability
Basic Probabilities and Set Theory
A&J © 2010. These flashcards were purchased by [Candidate P].
Pr Pr Pr PrA AB AC AD
n A n AB n AC n AD
Conditional Probability and Bayes Formula
A&J © 2010. These flashcards were purchased by [Candidate P].
Bayes Formula
Conditional Probability and Bayes Formula
A&J © 2010. These flashcards were purchased by [Candidate P].
Pr Pr | Pr
Pr |Pr Pr | Pr Pr | PrC C
AB B A AA B
B B A A B A A
Discrete Random Variables
A&J © 2010. These flashcards were purchased by [Candidate P].
Characteristics of Probability Mass Function
Discrete Random Variables
A&J © 2010. These flashcards were purchased by [Candidate P].
1. ( ) Pr( )f x X x
2. ( ) 0,f x x
3. ( ) 1x
f x
Discrete Random Variables
A&J © 2010. These flashcards were purchased by [Candidate P].
thk moment
Discrete Random Variables
A&J © 2010. These flashcards were purchased by [Candidate P].
: ( ) 0 : ( ) 0
( ) Prk k k
x f x x f x
E X x f x x X x
Discrete Probability Distribution
A&J © 2010. These flashcards were purchased by [Candidate P].
If X follows binomial distribution, find:
1. Probability Mass Function 2. Expected Value 3. Variance
Discrete Probability Distribution
A&J © 2010. These flashcards were purchased by [Candidate P].
The distribution is commonly represented by
~ Bin ,X n p , with Pr 1n xx
nX x p p
x
, where
0,1,...,x n , n and p are parameters for this distribution.
E X np 1Var X np p
Continuous Random Variable
A&J © 2010. These flashcards were purchased by [Candidate P].
Transformation of Random Variables
using
“CDF” Method
Continuous Random Variable
A&J © 2010. These flashcards were purchased by [Candidate P].
1 1Pr Pr PrY g X X g Y or X g Y
depending on the function, g
Continuous Random Variable
A&J © 2010. These flashcards were purchased by [Candidate P].
Transformation of Random Variables
using
“Inverse Transformation” Method
Continuous Random Variable
A&J © 2010. These flashcards were purchased by [Candidate P].
If Y g X , ' 0g X , x then the p.d.f of Y is
'
Y Xf y f h y h y , where 1h y g y
Continuous Probability Distribution
A&J © 2010. These flashcards were purchased by [Candidate P].
If X follows Exponential distribution, find:
1. Probability Density Function 2. Expected Value 3. Variance 4. Moment-Generating Function
Continuous Probability Distribution
A&J © 2010. These flashcards were purchased by [Candidate P].
1
, 0
0 , elsewhere
x
e xf x
0
11
x y x
F x e dy e
E X 2Var X
1
1XM t
t
Application of Probability in Risk Management
A&J © 2010. These flashcards were purchased by [Candidate P].
Relationship between the expected payment and the expected payment with deductible
Application of Probability in Risk Management
A&J © 2010. These flashcards were purchased by [Candidate P].
^E X E X d E X d
whereby,
0 0
^ ( ) ( )
d d
d
E X d xf x dx d f x dx S x dx
( )d d
E X d x d f x dx S x dx
Application of Probability in Risk Management
A&J © 2010. These flashcards were purchased by [Candidate P].
Coinsurance
Application of Probability in Risk Management
A&J © 2010. These flashcards were purchased by [Candidate P].
Payment 1 1E E X E X
Application of Probability in Risk Management
A&J © 2010. These flashcards were purchased by [Candidate P].
