Econometrics Notes

INTRODUCTORY ECONOMETRICS
Lectures 1 & 2
Statistics for Econometrics

POPULATION AND SAMPLE
Population – the group of ALL people or objects that are under study
Sample – a sub-set of the population
Parameter – a numerical characteristic of a population

1. Population & Sample Means
2. Expected Values
3. Population & Sample Variances
4. Population & Sample Covariances
5. Population & Sample Correlation Coefficients
6. Estimators

Statistic – a numerical characteristic of a sample
Statistical inference – drawing conclusion about a population based on information contained in a sample
Random sample – every sample of the same size in the population has the same chance of being selected

1

2

POPULATION MEAN AND SAMPLE MEAN

Set of all possible values of a random variable X

Parameters: population mean µ
2
population variance σ X

Given a random variable X (e.g. IQ scores, weights of all students, salaries of all workers, outcomes from tossing a die)
We consider a random sample of size n the sample containing n observations of X denoted by

x1 , x2 , x3 ....,xn
Sample mean = X =

Take many random samples of size n

1 n
∑ xi n i =1

Population mean of X =

µ

For each random sample of size n drawn from the population,
Statistics: sample mean
X
sample variance s 2

= E(X )

X

More on expected values later…
3

Set of all possible values X
…follows a normal distribution, if there are more than 30 random samples
4

1

EXPECTED VALUE OF A RANDOM VARIABLE X

EXPECTED VALUE OF A RANDOM VARIABLE X (continued)

Expected value of X = E(X)

If X is a continuous random variable:

E ( X ) = ∫All x x f ( x ) dx

If X is a discrete random variable: n E ( X ) = x1 p1 + ... + xn pn = ∑ xi pi

xi

i =1

= all possible values of X

f(x) = the probability density function, p.d.f

xi = all possible values of X pi = the probability associated with it n = the number of observations

Note