Assignment 5 ACTSC 433/833, Winter 2012
(Due at the beginning of the class on March 29)
For this assignment, if needed, you can use any software such as Maple, Mathematica, and MATLAB to nd roots of a
Solutions to Assignment 1 ACTSC 433/833, Winter 2012
1. (a) We know that M SEX () = V ar(X ) = n and M SES 2 () = V ar(S 2 ) = E (S 4 ) 2 .
Note that (n 1)S 2 = n=1 (Xi X )2 = n=1 Yi2 nY 2 , where Yi
SOLUTIONS TO TEST # 1 ACTSC 433/833, WINTER 2012
1. (a) The distribution function of X(n) is
0,
FX(n) (x) =
1,
x2n
,
2n
x < 0,
0 x < ,
x .
Thus, E (n ) = 0 (1 FX(n) (x)dx = 1
asymptotically unbiased
ACTSC 433/833 Winter 09 Assignment 2 Due: 10 March 2009 (hand in to the instructor at the beginning of class)
1. You are given the following censored and truncated data: I 1 2 3 4 5 6 7 8 di 0 0 0 2.5
Assignment 2 ACTSC 433/833, Winter 2012
(Due at the beginning of the class on February 9)
1. Let X1 , ., Xn be a random sample from the distribution function F (x) = 1 S (x) and
Fn (x) be the empirica
Assignment 3 ACTSC 433/833, Winter 2012
(Due at the beginning of the class on March 1)
1. You are given the following ages at time of death for 10 individuals: 38, 45, 52, 52, 56,
59, 68, 70, 74, and
Outline
ACTSC 433/833 Winter 09 Chapter 11 Contemporary Issues Part II Stochastic Mortality Models
Johnny Li
Department of Statistics and Actuarial Science, University of Waterloo
March, 2009
Outline
Assignment 1 ACTSC 433/833, Winter 2013
(Due at the beginning of the class on January 22)
1. Let X1 , X2 , X3 be a sample of size 3 from the uniform distribution U ( 2, + 2), where
2. Let X(2) be the
Assignment 2 ACTSC 433/833, Winter 2013
(Due at the beginning of the class on January 31)
1. Let X1 , ., Xn be a random sample from the distribution function F (x) = 1 S (x) and
Fn (x) be the empirica
Assignment 1 ACTSC 433/833, Winter 2012
(Due at the beginning of the class on January 19)
1. Let X1 , ., Xn be a sample of the random variable X that has a Poisson distribution with
mean > 0.
(a) Calc
SOLUTIONS TO MIDTERM TEST # 2 ACTSC 433/833,
WINTER 2012
1. (a) The kernel density estimate for the probability that an individual aged 90 will survive
at least 3 years using the uniform kernel with b
Outline
ACTSC 433/833 Winter 2009 Chapter 13 Contemporary Issues Part III Mortality Derivatives
Johnny Li
Department of Statistics and Actuarial Science, University of Waterloo
April, 2009
Outline
Out
Outline
ACTSC 433/833 Winter 09 Chapter 11 Contemporary Issues Part I What Is Longevity Risk?
Johnny Li
Department of Statistics and Actuarial Science, University of Waterloo
March, 2009
Outline
Outli
ACTSC 433/833 Analysis of Survival Data
Johnny S.H. Li
Department of Statistics and Actuarial Science, University of Waterloo
January 6, 2009
Why ACTSC 433/833? About the Course About the Instructor
A
Assignment 4 ACTSC 433/833, Winter 2012
(Due at the beginning of the class on March 15)
1. Four losses are observed with values 96, 135, 278, and 396. Six other losses are known to
be less than 90. Lo
Solutions to Assignment 4 ACTSC 433/833, Winter 2012
1. (a) We have f (x) = F (x) =
/x
e
,x
x2
> 0. Thus,
L() = f (96)f (135)f (278)f (396)(F (90)6 4 e0.0906131 .
It follows from
d ln L()
d
= 0 that
Solutions to Assignment 5 ACTSC 433/833, Winter 2012
1. (a) For Line 1: S1 (x) = S0 (x) and f1 (x) = 100 , x > 100. For Line 2: S2 (x) = (S0 (x)b
x+1
b100b
and f2 (x) = xb+1 , x > 100, where b = e . T
Assignment 3 ACTSC 433/833, Winter 2013
(Due at the beginning of the class on February 26)
1. Let S (t) be the Product-Limit estimator for the survival function S (t).
Calculate Cov (S (yj ), S (yj +1