PSTAT 175:
Assignment # 1
Due Tuesday, October 4, 2016.
This assignment is due in lecture on Tuesday.
1. (a) A Binomial experiment observes X =the number of successes in n independent trials. The probability mass function is f (x) = nx px (1 p)nx if the p
PSTAT 175:
Solutions Assignment #2
October 21, 2016
1. We can calculate the variance of a hypergeometric distribution via
(a) We have n1 subjects in one group and n2 subjects in the second group. We choose m of these
subjects at random. Conditional on the
Stratification
Drew Carter
November 15, 2016
Age and Lung Cancer Survival
coxph(Surv(time, status) ~ age, data = lung)
#
#
#
#
#
#
#
#
Call:
coxph(formula = Surv(time, status) ~ age, data = lung)
coef exp(coef) se(coef)
z
p
age 0.0187
1.0189
0.0092 2.03 0
Lab C: Cox Regression
Drew Carter/Sergio Rodriguez
October 18, 2016
For this lab the relevant commands are:
survdiff: Tests if there is a difference between two or more survival curves.
coxph: Fits a Cox proportional hazards regression model;
as well as
PSTAT 175:
Solutions to Assignment # 3
November 9, 2016
1. For a proportional hazards model with a continuous covariate xi , we have a hazard function
h(t | xi ) = h0 (t) exp [xi ]
(a) If we adjust the covariates by subtracting off a constant, xi = xi a,
PSTAT 175:
Greenwoods Formula
October 6,2016
Reading
Survival Analysis: A Self-Learning Text Kleinbaum and Klein. Chapter 2 pp. 5867 and pp.7881.
KM estimator gives us estimates of S(t) for any t from 0 up to the largest observation. How do we use
this?
PSTAT 175:
Comparing Two Samples
October 21,2014
Reading
Survival Analysis: A Self-Learning Text Kleinbaum and Klein. Chapter 2 pp. 6771.
Confidence Interval
We argued that
Var(log(S(t)
k
X
j=1
mj
= Vt
nj (nj mj )
where k is the index associated with t(k
PSTAT 175:
Checking the Proportional Hazards Assumption
November 1, 2016
Reading
Survival Analysis: A Self-Learning Text Kleinbaum and Klein. Chapter 4 pp. 161183.
Proportional Hazards Assumption
The assumption is that the thing we are interested in is t
PSTAT 120C
Winter 2016
Midterm
2/9/2016
Time Limit: 70 Minutes
Name:
Teaching Assistant
This exam contains 4 pages (including this cover page) and 3 questions.
Total of points is 100. Do not ask questions during exam. Keep your eyes on your own paper
at a
PSTAT 120C:
Solutions to Practice Midterm Questions
April 27, 2010
1. 15.4 (a) There are 7 out of 10 of the twins where student A did better than student B. The
probability of this occurring is
10
10
10
10
176
10
Pcfw_M 7 = 2
+
+
+
= 210 (120 + 45 + 10
Lesson 10: Conditional densities, probabilities, moments. Covariance.
Examples.
Example 1. A company offers a basic life insurance policy to its employees, as well as
supplemental life insurance policy. To purchase the supplemental policy, an employee
mus
SECTION 1. The Measurement of Interest
Summary of Concepts and Formulas in Sections 1a(i) to 1a(v)
(1) The accumulation function a(t) is the AV at time t of $1.00 invested at time 0.
(2) The effective rate of interest in the th year is based on the amount
Lesson 9: Joint density calculations for random vectors. Examples.
Example 1. A company is reviewing tornado damage claims under a farm insurance
policy. Let X be the portion of a claim representing damage to the house and let
Y be the portion of the same
PSTAT W 182T
Solutions for Homework #6
Summer 2015
Homework 6: Important Distributions Part 2.
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Wednesday, 8/26/2015. Please write full solution
Lesson 10: Conditional densities, probabilities, moments. Covariance.
Methodology.
DEFINITIONS AND FACTS RELATED TO PROBABILITIES AND DENSITIES:
For any two random variables X and Y with the joint probability density function
(joint pdf ) fX,Y (x, y)
P (
PSTAT W 182T
Homework Assignment #7
Summer 2015
Homework 7: Joint Density Calculations for Random Vectors.
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Sunday, 8/30/2015. Please write full
Lesson 9: Joint density calculations for random vectors.
Methodology.
A. Definitions.
For any two random variables X and Y, the joint cumulative probability distribution function (joint cdf ) is defined as
FX,Y (a, b) = P (X a, Y b), < a, b < .
We say t
Lesson 8: Joint Discrete Random Variables
Examples.
Example 1. An insurance contract reimburses a familys automobile accident losses
up to a maximum of two accidents per year. The joint probability distribution for the
number of accidents a three person f
PSTAT W 182T
Homework #4
Summer 2015
Homework 4: Transformations of Single Random Variables.
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Wednesday, 8/19/2015. Please write full solutions.
PSTAT W 182T
Homework Assignment #8
Summer 2015
Homework 8: Joint Density Calculations for Random Vectors.
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Sunday, 8/15/2015. Please write full
Lesson 1: Insurance terminology:
insurance policy, deductibles and policy limits.
Translating a word problem into a random variable Y=g(X).
1
How Insurance Policy Works.
The insurance policy. Although there are many different types of insurance, the basi
PSTAT W 182T
Homework Assignment #2
Summer 2015
Homework 2:
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Wednesday, 8/12/2015. Please write full solutions. Try all problems and include
par
Lesson 8: Joint Discrete Random Variables
Definitions and Formulas.
We shall review the joint discrete random variables. The problems from this topic include computations of (conditional) moments, determination of constants, and posterior distribution.
1
Homework 1: Interest Theory & Basic Annuity
Fall 2016
Instructor: Yanjiang Guo (Zak)
Due Date: Tues, January 24, 2017
INTEREST THEORY:
Problem 1:
Problem 2:
Problem 3:
Problem 4:
Problem 5:
BASIC ANNUITY:
Problem 6:
Problem 7:
Problem 8:
Problem 9:
Proble
PSTAT W 182T
Homework Assignment #3
Summer 2015
Homework 3:
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Sunday, 8/15/2015. Please write full solutions. Try all problems and include
partia
PSTAT W 182T
Homework Assignment #1
Summer 2015
Homework 1: Mixed Distributions and Insurance Terminology
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Sunday, August 8, 2015. Please write
PSTAT W 182T
Solutions for Homework #5
Summer 2015
Homework 5: Important Distributions Part 1.
Instructions: Solutions to these problems should be submitted in pdf format on class Gaucho Space
by 11:30pm on Sunday, 8/24/2015. Please write full solutions.