Random Variable
We can define a random variable for a quantity of interest by assigning a numerical value to each event in asample space. The sum of the probabilities for all values of a random variable is.
Example 1:
In an experiment of tossing a coin twice, the sample space is
.
In this experiment, we can define random variable总数of tails. Thentakes the valuesand.
The table illustrates theprobability distributionfor the above experiment.
The notationis usually used to represent the probability of a random variable, where theis random variable andis one of the values of random variable.
is read as "The probability thatequalsis 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.
Example 2:
A dart is thrown at a dartboard of radiusinches. If it misses the dartboard, the throw is discounted. Define a random variableas the distance in inches from the dart to the center.