We can define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space . The sum of the probabilities for all values of a random variable is .
In an experiment of tossing a coin twice, the sample space is
In this experiment, we can define random variable as the total number of tails. Then takes the values and .
The table illustrates the probability distribution for the above experiment.
The notation is usually used to represent the probability of a random variable, where the is random variable and is one of the values of random variable.
is read as "The probability that equals is one-fourth."
The above definition and example describe discrete random variables... those that take a finite or countable number of values. A random variable may also be continuous, that is, it may take an infinite number of values within a certain range.
A dart is thrown at a dartboard of radius inches. If it misses the dartboard, the throw is discounted. Define a random variable as the distance in inches from the dart to the center.