Working with Working with Random VariablesRandom 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 – 15000 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