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Random Variable

Suppose a coin is tossed ten times. The head can shown 0, 1, 2, 3, ...., 10 times. Similarly, the tail can also shown 0, 1, 2, 3, ...., 10 times. Suppose, head is shown six times and tail is shown four times. If we repeat the experiment the values of these variables (head and tail) can change (in most cases it is changed). So in this case, head and tail are two random variables whose values are changed from trial to trial as experiment is repeated.

Definition
A random variable is a function whose value is subject to change with every outcome of an experiment.

For example, a coin is tossed ten times.

Experiment: 1
Random Variable H = 6
Random Variable T = 4

Experiment: 2
Random Variable H = 3
Random Variable T = 7

Experiment: 3
Random Variable H = 1
Random Variable T = 9

Range of a Random Variable
Range of of random variable is the set of all possible values a random variable can take. For example in the above experiment,

Range(H) = {0,1,2,3,4,5,6,7,8,9,10}
Since Head (H) can appear from 0 to 10 times. Similarly,

Range(T) = {0,1,2,3,4,5,6,7,8,9,10}
As Tail (T) can also appear from 0 to 10 times.

RELATED PAGES
- Random Variable
- Stochastic Process