INTRODUCTION TO ECONOMETRICS II
ECO 306
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1.1.2.0 OBJECTIVE The main objective of this unit is to provide abroad understanding of the topic, Random Variables, and Sampling Theory, which is preparatory to the more widely used simple and multiple regression analyses.
1.1.3.0 MAIN CONTENTS
1.1.3.1 Random Variables and Sampling Theory
A variable X is said to be a random variable if for every real number a there exist a probability
(
)
P X
a
that X takes on a valueless than or equal to a. That is, a Random variable is a variable whose value cannot be predicted exactly. It can assume any value. Random variables could be discrete or continuous. A discreterandom variable is one that has a specific set of possible values or a finite set of values. An example is a total score when two dice are thrown. A continuous variable, e.g. the temperature in a particular room, is a variable that can assume any value in thecertain range. It can take any form of the continuing range of values.
The set of all possible values of a random variable is known as apopulation where thesample or a random variable can be drawn for inferential analysis.
1.1.3.2 Expected values of discrete random variable
The expected value of a discrete random variable is the weighted average of all its possible values, taking the probability of each outcome as its weight. It can be calculated by multiplying each possible value of the random variable by its probability and adding. In mathematical terms, if X denotes the random variable, its expected value is denoted by E(X). Let us suppose that X can take nparticular values of, and that the probability of is
Then,
1
( )
...[1.01]
n
i
i
n
n
i
i
i
E X
x p
x p
x p
Table 1.0 shows an example of expected value of variable X with two dice.
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