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HW-pgs. 470-471 (7.2-7.6, skip 7.4)
7.1 Quiz Friday 12-6-13
www.westex.org HS, Teacher Website
12-4-13
Warm up—AP Stats
If you toss a coin 4 times what are the possible
outcomes? List them out. (DON’T BE LAZY!!!)
http://sportsillustrated.cnn.com/vault/article/mag
azine/MAG1206508/index.htm
Name _________________________
AP Stats
7 Random Variables
7.1 Discrete & Continuous Random Variables
Date _______
Objectives
 Define a discrete random variable.
 Explain what is meant by a probability distribution.
 Construct the probability distribution for a discrete random variable.
 Given a probability distribution for a discrete random variable, construct a probability
histogram.
Introduction
Think about the sample space when we toss four coins (our warm up). One possible outcome is
HTHT. How many outcomes in total are in the sample space? _____
In statistics it is interesting to ask what is the count of heads (or tails) in the four tosses.
For example, Let X be the number of heads in four tosses. Looking back at our first outcome
X = 2. If the next outcome is HHHH, the value of X changes to X = 4. What are the possible
values of X? ________________ So tossing a coin four times will give X one of these
possible values. We call X a _________ ____________ because its value varies when the
coin tossing is repeated. A random variable is a variable whose value is a _______________
outcome of a random phenomenon. Random variables are denotes by CAPITAL letters near the
end of the alphabet, such as X or Y. Knowing the mean of a random sample, x is of great
interest. When a random variable X describes a random phenomenon (as above), the sample
space S is the list of possible values of the random variable. In the case above,
__________________. We now have to assign probabilities to events. We will do so for
__________ and _______________ (tomorrow) random variables.
Discrete Random Variables
So far we have only one way to assign probabilities: State the probabilities of the individual
outcomes and assign probabilities to events by summing over the outcomes. Ex. When rolling
a standard die, P(1 or 6). First we find the prob. of outcome of a 1 and the prob. of outcome
of a 6. Then we find the probability of the EVENT of getting a 1 or a 6 by SUMMING the
probability of the OUTCOME of a 1 and the probability of the OUTCOME of a 6.
1
1
1
P(1 or 6) =
+
= . In all of the situations we did in Ch. 6 the outcome probabilities must
6 6 3
be between 0 and 1, and their sum must be 1. When the outcomes are numerical, they are
values of a random variable. We will call such random variables having probability assigned in
this way ____________ __________ _______________.
A discrete random variable X has a _______________ number of possible values. (think
about tossing the coin 4 times.) The ______________ _______________ of a discrete
random variable X lists the values and their probabilities:
Values of X:
Probability:
x1
p1
x2
p2
x3
p3
...
...
x1
pk
The probabilities pi must satisfy two (obvious) requirements:
1. Every probability pi is a number between ___ and ___.
2. The sum of the probabilities is ___: p1 + p1 + . . . + pk = 1
Find the probability of any event by adding the probabilities pi of the particular values xi that
make up the event.
Ex. There are 5 possible values of X for tossing a coin 4 times. What is the probability of
each?
Values of X:
_____
_____
_____
_____
_____
Probability:
_____
_____
_____
_____
_____
Question---What is the probability that 3 or more heads will show up if 4 coins are tossed?
(Isn’t it just the sum of the probabilities of getting 3 or 4 heads?) In the language of random
variables:
P(X  3) = P(X = 3) + P(X = 4)
=
Question---What is the probability of getting 1 or more heads when 4 coins are tossed?
Read below to learn about probability histograms.
Construct a probability histogram using our example of tossing a coin 4 times and seeing the
probability of our Random Variable X (# of heads obtained in the 4 tosses).
7.4 Housing in San Jose, I-How do rented housing units differ from units occupied by their
owner? Here are the distributions of the number of rooms for owner-occupied units and
renter-occupied units in San Jose, California:
Number of Rooms
1
2
3
4
5
6
7
8
9
10
Owned 0.003 0.002 0.023 0.104 0.210 0.224 0.197 0.149 0.053 0.035
Rented 0.008 0.027 0.287 0.363 0.164 0.093 0.039 0.013 0.003 0.003
Make probability histograms of these two distributions, using the same scales. What are the
most important differences between the distributions of owner-occupied and rented housing
units?
Owned
Rented