Lecture 15-2 / Random Variable/ 2018-2019

Random Variable
It is a function that is defined on the probability space as
follows:

Therefore if it takes its values from countable set it is called
discrete random variable, d.r.v., otherwise it is called
continuous random variable, c.r.v. that is if its values taken
from uncountable set.

That is a r.v. takes countable values , then it is d.r.v. and probability
That is a r.v. takes countable values , then it is d.r.v. and probability
of its values is called probability mass function.
EXAMPLE:
Select items at random from a batch of size N until the ?rst defective item is found. Record the number of non-defective items.
Sample Space: S = {0,1,2,...,N}
The result from the experiment becomes a variable; that is, a quantity taking di?erent values on di?erent occasions.
Because the experiment involves selection at random, we call it a random variable. Abbreviation: rv. Notation: capital letter, often X. Definition( Random Variable)
The random variable X is the function that is can be defined as:
X:??R
R is the set of possible values that a random variable (rv) X can take is called the range of X.
Definition( Discrete Random Variable)
A rv X is said to be discrete if its range consists of a ?nite or countable number of values.
Definition( Continuous Random Variable)
A rv X is said to be continuous if its range consists of a ?nite or uncountable number of values.
Examples: based on tossing a coin repeatedly, No. of H in 1st 5 tosses: {0,1,2,....,5}. No. of T before ?rst H: {0,1,2,....}
Probability Distributions or ‘How to describe the behaviour of a rv’