Working with Random Variables

What is a Random Variable? A random variable is a variable that has a numerical value which arises by chance (ie – from a random event). –Numerical scores or values may be assigned to events to create a random variable. For example, in attempting to test the hypothesis that “whenever I drop my toast it always falls buttered side down!” one could let “down” = 1 and “up” = 0.

Discrete and Continuous If there is a finite number of possible values that variable can take it is considered to be discrete. If there is an infinite number of possible choices, the variable is considered continuous. If there is a huge number of possible values that a discrete variable can take we can often act as if it is continuous.

Graphing Probability Distributions A histogram gives you a quick picture of the possible outcomes of an event. For example, suppose you rolled 3 dice, 5000 times! What would you expect the sum of the dice to equal? –What would be the most probable sum? –What would a graph (histogram) of all sums look like?

3-Dice Experiment

How about 20 Dice!

20 Dice – times!

Working With Continuous Variables What is the probability of either A or B happening? What is the probability of neither happening?

Z-Scores: a new twist We can use z-scores to tell us probability values As we have just seen, many discrete processes can be “modelled” as normal distributed ones

In conclusion… Key idea here is the notion of a probability distribution and how area relates to probability Make sure you grasp the “re- interpretation” of z-scores that we have developed here Try…4.43, 4.44, 4.47, 4.52, 4.54, 4.55