ST2132 (SUPP)
Discrete Distributions
p(k)
k
E(X)
Var(X)
M (t)
Binomial
n k
p (1 p)nk
k
0, 1, . . . , n
np
np(1 p)
(1 p + pet )n
Geometric
p(1 p)k1
1, 2, . . .
1
p
1p
p2
r, r + 1, . . .
r
p
r(1 p)
p2
pet
1 (1 p)et
r
pet
1 (1 p)et
0, 1, . . .
expcfw_(et 1

Part II
Sampling Distributions
6
Distributions Derived from the Normal Distribution
Ch 6
Overview
We study the 2 , t, and F distributions as they occur in many statistical problems.
The 2 Distribution
Definition 8. If Z is a standard normal random variabl

If we let X1 , X2 , X3 denote the counts in the three cells and let n = 1029, the log likelihood
of is
.
`() = X1 log(1 )2 + X2 log 2(1 ) + X3 log 2
.
= (2X1 + X2 ) log(1 ) + (X2 + 2X3 ) log .
Setting the derivative to zero, we have
2X1 + X2 X2 + 2X3
+
=0

Part I
Review of Probability
1
Probability
Ch 1
Overview
Probability theory is concerned with situations in which the outcomes occur randomly.
It is therefore useful as a mathematical model for chance phenomena.
Throughout this module we will see many exa

Question 3:
If you are told that you scored in the 80th percentile, from just this information would
you know exactly what that means and how it was calculated? Explain.
Answer :
It means that 80% of other people who took the test scored less than me and

Question 9:
The formula for finding each student's test grade (g) from his or her raw score (s) on a
test is as follows: g = 16 + 3s.
Is this a linear transformation? If a student got a raw score of 20, what is his test
grade?
Answer :
This is an example

ABRIDGED LIFE TABLES
o The complete life tables for humans are very long and laborious to com-
pute.
0 They have around 120 rows. Even though they are very detailed, often
at least for demographic purposes such a detailed information is not
required.
0 Fo

MORTALITY
o The word mortality relates with the event of death.
a Rates and probabilities measuring mortality describes the nature of nat—
ural decrease in the population.
0 The crude and age specific mortality rates are regularly calculated for
many co

MORTALITY
o The word mortality relates with the event of death.
a Rates and probabilities measuring mortality describes the nature of nat—
ural decrease in the population.
0 The crude and age specific mortality rates are regularly calculated for
many co

Construction of Nuptiality Tables for the Single Population in India: 1901-1931
Author(s): C. R. Malaker
Source: Demography, Vol. 10, No. 4 (Nov., 1973), pp. 525-535
Published by: Springer on behalf of the Population Association of America
Stable URL: htt

MULTIPLE-DECREMENT LIFE TABLES: lNTRODUCTION
0 So far all life tables we have looked at considered only one reason of
death. A person was either alive or dead. Once a person dies he, or she
does not return (ie. death is an absorbing state). Eventually eve

POPULATION PROJECTION
o In most countries census is conducted every ten years. Ideally, a cen—
sus should provide an accurate enumeration of the population and any
measure related to the population in the census year.
0 However, often estimates for non-

ESTIMATING lqa; FROM 1mg;
0 In principle two types of rates lqm and 1mm need not be related.
0 Under certain assumptions however, a theoretical relationship can be
denved. -
0 We make the following assumptions:
1. Mortality only varies with age, and not w

THE ANALYSIS OF FERTlLlTY
o In demography the term fertility refers to the actual number of children
born alive. It refers to actual reproductive performance, not possible
performance.
0 The physiological ability to bear children is called fecundity, this

SOME CHARACTERISTICS OF THE STABLE POPULATION
0 We have shown that the size of the population aged between a: and 50+ 1
last years is given by (1 +r)_($+'5)1Lm. From this formula the average
age of the population can be calculated.
0 If 1mm is the prevail

THE STANDARDISED DEATH RATE
0 So how do we compare the mortality experience of two populations with
a single number.
a One obvious possibility is to assess the impact of a set of age—specific
death rates on a standard population age structure.
o This proc

Part III
Estimation
7
Estimation of Parameters and Fitting of Distributions
Ch 8
Overview
Many families of probability laws depend on a small number of parameters.
Unless the values of the parameters are known in advance, they must be estimated from data