A random variable
represents the possible outcomes we could observe on measuring some quantity.
Ransdom variables can be either discrete or contionuous. A discrete random variablehas possible values
The number of possible values thatcan take might be finite or infinte.
The number of brothers and sisters a person has is a discrete random variable. This is obviously a finite number, even if their parents are rabbits.
The number of times a person may throw a six in all the games of chance they ever play is also discrete. There is no upper limit to the possible number of sixes that may be thrown, but the number of sixes thrown must be a whole number.
Note that being discrete need not mean being an integer. The money in you wallet or purse must be a multiple of the smallest currency unit. In England, if I have two pounds 20 pence that is 2.2 pounds.
A continuous random variablehas all possible values in some interval, which may be finite or infinite.
A person may weigh anything between 0.5 Kg to 500 Kg – yes really. The heaviest person ever recorded weighed 635 Kg.
The distance to the travelled by a photon between being emitted by a star and being absorbed is anything from zero to infinity.
Whether a distribution is discrete or continuous, if the range of values is infinte, as values become bigger, the probability of the random variable taking that value must decrease. This is so that the prabilities sum to one.