Not just Pinkie Pie, outcomes of events that involve some level of uncertainty are also random. A random variable describes these outcomes as numbers. Random variables can take on different values; just like variables in math taking different values.
If the possible outcomes are distinct numbers (e.g. counts), then these are called discrete random variables. If the possible outcomes can take on any value on the real number line, then these are called continuous random variables.
There are six possible outcomes (1, 2, 3, 4, 5 and 6) when you roll a dice. Each number is distinct. We can assume X as a random variable that can take any number between 1 and 6; hence it is finite and discrete. For any single roll, we can assume x to be the outcome. Notice that we are using uppercase X for the random variable and lowercase x for the value it takes for a given outcome.
X is the set of possible values and x is an observation from that set.
In lesson 20, we explored the rainfall data for New York City and Berkeley. Here, we can assume rain to be a continuous random variable X on the number line. In other words, the rainfall in any year can be a random value on the line with 0 as the lower limit. Can you guess the upper limit for rainfall? The actual data we have is an outcome (x); observation; a value on this random variable scale. Again, X is the possible values rainfall can take (infinite and continuous), and x is what we observed in the sample data.
In lesson 19, we looked at SAT reading score for schools in New York City. Since SAT reading score is between 200, the participation trophy and 800, in increments of 10, we can assume that it is finite and discrete random variable X. Any particular score we observe, for instance, 670 for a student is an observed outcome x.
If you are playing monopoly, the outcome of your roll will be a random variable between 2 and 12; discrete and finite; 2 if you get 1 and 1; 12 if you get 6 and 6, and all combinations in between.
In lesson 14, we plotted the box office revenue for STAR WARS films. We can assume this data as observations of a continuous random variable.
Do you think this random variable showing revenue can be negative? What if they lose money? Maybe not STAR WARS, but there are loads of terrible films that are negative random variables.
Can you think of other random variables that can be negative?
How about the national debt?
Are you old enough to have seen a surplus?
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We ran federal surpluses from 1998 to 2001. Then Bush Jr.’s tax cuts took us from the largest surplus to to largest deficit in history. As for a Treasury surplus, I’m not sure if that ever happened.