Transcript Working with Random Variables

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 – 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 “reinterpretation” of z-scores that we have
developed here
• Try…4.43, 4.44, 4.47, 4.52, 4.54, 4.55