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Random Variable

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 1 .

Example 1:

In an experiment of tossing a coin twice, the sample space is

{HH, HT, TH, TT} .

In this experiment, we can define random variable X as the total number of tails. Then X takes the values 0 , 1 and 2 .

The table illustrates the probability distribution for the above experiment.

Number of Tails ( X ) 0 1 2 Probability 1 4 1 2 1 4

The notation P ( X = x ) is usually used to represent the probability of a random variable, where the X is random variable and x is one of the values of random variable.

P ( X = 0 ) = 1 4 is read as "The probability that X equals 0 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.

Example 2:

A dart is thrown at a dartboard of radius 9 inches. If it misses the dartboard, the throw is discounted. Define a random variable X as the distance in inches from the dart to the center.

0 X < 9

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