What is Random Variable?
When there is a probability associated with a variable that makes it Random Variable.
So a Random variable can take many different values with different probabilities.
Q.1) No. of Days in a week-: Is this a Random Variable?
A.1) NO, because no. of days in a week is fixed i.e 7
Q.2) No. of Days in a Month-: Is this a Random Variable?
A.1) Yes, because no. of days in a month can be 28,29,30 or 31. So this is Random in nature.
Suppose X is "Something" now it can take value "0" if 3 comes up on a Dice and "1" if even no. comes up on dice.
So we know that probability of getting a 3 on Dice is 1/6 . So probability of getting a value "0" is 1/6
Similarly the probability of getting an Even no. on dice is 1/2. So probability of getting "1" is 1/2.
so we see that when "something is attached with different values along with different probabilities it becomes a Random variable.