RANDOM VARIABLES
&
PROBABILITY DISTRIBUTIONS
, Introduction
In order to make valid statements about random phenomena, it is required that e
of the possible outcomes of. a random experiment be represented by a real numb
rather. than its physical description..
The representation of outcomes of a random experiment by use of real numbers l
to the notion of a random variable.
, Random variable
A random variable is any rule that assigns a numerical value to each
outcome in sample space S .
It is a function whose domain is the sample space S and whose range is
the set of real numbers .
, The numerical value can be the same for several outcomes of the
experiment.
Given that outcomes can not be predicted with certainty, it implies that
random variable to cannot be predicted with certainty.
Remark: Random variables are usually denoted by uppercase letters,
such as X and Y, and lower case letters as x and y, denote some particular
value of the corresponding random variable.
&
PROBABILITY DISTRIBUTIONS
, Introduction
In order to make valid statements about random phenomena, it is required that e
of the possible outcomes of. a random experiment be represented by a real numb
rather. than its physical description..
The representation of outcomes of a random experiment by use of real numbers l
to the notion of a random variable.
, Random variable
A random variable is any rule that assigns a numerical value to each
outcome in sample space S .
It is a function whose domain is the sample space S and whose range is
the set of real numbers .
, The numerical value can be the same for several outcomes of the
experiment.
Given that outcomes can not be predicted with certainty, it implies that
random variable to cannot be predicted with certainty.
Remark: Random variables are usually denoted by uppercase letters,
such as X and Y, and lower case letters as x and y, denote some particular
value of the corresponding random variable.
