To understand random variable first you have to know about events. I will make you understand using examples.
What are events?
Tossing three coins on which one head turns up
A random variable quantify events of occurence.
In other words, a random variable X is a function from set of events to real number.
Suppose S is set of events then X : S->R
If you toss four coins the possible out comes are
make a statement that two atleast one head turns up
Probability Distribution Function (PDF)-
“Different values of random variable togethor with their probabilities form probability distribution”
(Operations Research S. D. Sharma)
In other words, P is a Probability Distribution Function (PDF) defined as P : X(e)-> [0,1], where e is set of events.
Properties of the probability distribution function
2 – Summation of all probabilities is 1 i.e ∑∞i=0 P(xi)=1