Lecture 15

Random Variable
Experiments whose outcomes are numbers
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:
The set of possible values that a random variable X can take is called the range of X.
The set of possible values that a random variable (rv) X can take is called the range of X.
Definition:
A rv X is said to be discrete if its range consists of a ?nite or countable 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,....}
Note: although the de?nition of a discrete rv allows it to take any ?nite or countable set of values, the values are in practice almost always integers.
Probability Distributions
or ‘How to describe the behaviour of a rv’