Random variable

Summary

• An experiment is any procedure that will result in precisely one outcome from a well-defined set of possible outcomes. Example : Tossing a dice will result in one element in the set \(\{ 1,2,3,4,5,6 \}\) .
• A random variable is a variable whose value is not observed until the experiment has been performed (note: this is a simplified version of the actual definition of a random variable). Example : Flip a coin five times and let a random variable \(X\) denote the number of tails. If the experiment results in “ HTTHT ” , the random variable takes the value \(x=3\) .
• The range of a random variable is the collection of all values that a random variable can take.
• Two important types of random variables:
• If the range of the random variable is a finite set, we call it discrete
• If the range of the random variable is an interval, we call it continuous
• Note 1: these are not the definitions of discrete and continuous random variables
• Note 2: there exists random variables that are neither discrete nor continuous