ACTU 5823 Fall 2016
Assignment 2
Assignment 2
1. Losses follow a lognormal distribution with = 7 and = 1. Losses are subject to a franchise deductible
of 1000 and a maximum covered loss of 10,000.
Calculate the expected value of the payment random variabl
W4440 Homework 5 Solution
Shuaiwen Wang
Problem 7.1
Pt
Proof. Since yt = y0 + i=1 ci , we have
Pt
a. Eyt = y0 + i=1 Eci = y0 + tc ;
Pt
b. Varyt = i=1 Varci = tc2 .
Problem 7.2
Proof. a. Notice that we have yT +` = yT + `
c, we have
yT +` yT +` =
`
X
cT +i
W4440 Homework 4 Solution
Shuaiwen Wang
1. Data sat
We do the regression and by using the summary() function we got the following result,
Figure 1: summary() of the regression total expend + salary + ratio + takers.
from this we can see that only takers i
CALCULUS I - WRITTEN HOMEWORK 0 - DUE 9/9/14
PAUL SIEGEL, INSTRUCTOR
Problem 1 (Algebra). Solve the equation
2
x
5
x
= 2.
Problem 2 (Algebra). Find all values of x for which the following inequality holds:
x+5
x1>
x+1
Problem 3 (Analytic Geometry). Sketch
CALCULUS I - WRITTEN HOMEWORK 1 - DUE 9/16/14
PAUL SIEGEL, INSTRUCTOR
Problem 1. For each of the following pairs of functions f, g, find a sequence of transformations which passes
from the graph of f to the graph of g. Sketch a graph of f and g.
2
2
(b) f
CALCULUS I - WRITTEN HOMEWORK 2 - DUE 9/23/14
PAUL SIEGEL, INSTRUCTOR
3
1 1
1
Problem 1. Consider the function f (x) = 4x4x
(x).
6 +1 defined on the domain [ 2 , 2 ]. Find a formula for f
(You may check your answer using graphing software if needed.)
Prob
GRAPHING RATIONAL FUNCTIONS WITH LIMITS
PAUL SIEGEL, INSTRUCTOR
In these notes we will review how to sketch the graph of a rational function using limits. Limits can help
detect the end behavior of a function (i.e. the shape of its graph at ) as well as t
Calculus I,
Columbia
University,
Fall 2014
Instructor:
Paul Siegel
Calculus I, Columbia University, Fall 2014
Instructor: Paul Siegel
October 6, 2014
Calculus I,
Columbia
University,
Fall 2014
What you should know
Instructor:
Paul Siegel
Algebra (e.g. so
Actuarial Models Fall 2015
Assignment 11
Assignment 11
1. Policyholders are in one of 2 classes, A or B. You are given the following distributions for claim counts
and sizes:
Class A
Claim counts
Claim sizes
Count Probability Size Probability
0
0.8
100
0.
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Actuarial Models Fall 2015
Solutions to Assignment 12
Solutions to Assignment 12
1. We can use the uniform exposure formula, using n = 2 when calculating Z .
x1 = 55
v1 = 50
x2 = 75
x3 = 80
= x = 70
v2 = 50
v3 = 200
v = 100
(55 70) + (75 70) + (80 70)2 1
Calculus I,
Columbia
University,
Fall 2014
Instructor:
Paul Siegel
Calculus I, Columbia University, Fall 2014
Instructor: Paul Siegel
December 12, 2014
Calculus I,
Columbia
University,
Fall 2014
The Derivative of a Function
Instructor:
Paul Siegel
Limits