Download Guided Reading page 341 – 344

Section 6.1: Discrete and Continuous Random Variables
AP Statistics – Guided Reading
Name: _______________________
Date: ______________ Period: ___
Directions: Begin on page 341 and end on page 343.
1) What is the sample space for flipping a fair coin 3 times?
2) Since there are _____ equally likely outcomes, the probability is ______ for each possible
outcome.
3) Define the variable X = ___________________________________________________. The value of
X will _________________________________________________________ but will always be one
of the numbers _______________________________.
4) How likely is X to take each of those values? Group the possible outcomes by the number of
heads obtained as in the textbook:
________
X=0
________
X=1
________
X=2
_________
X=3
5) Fill in the probability distribution of X:
X (total number of
heads)
Probability P(X)
*Note: You have seen probability distributions in the last chapter. It is the same thing as a
probability model.
6) Sketch a graph of the probability distribution as a histogram. Describe what you see in terms
of shape.
P(X)
Number of Heads
7) What’s the probability that we get at least one head in three tosses of the coin? Write in
symbols and then calculate that probability.
8) A random variable takes _____________________________________________________________
___________________________________________________________________________________.
The probability distribution of a random variable ______________________________________
___________________________________________________________________________________.
9) We usually denote random variables by capital letters near the end of the alphabet, such as X
or Y.
10) There are two types of random variables: _____________________ and
__________________________.
11) If we can find a way to list all possible outcomes for a random variable and assign probabilities
to each one, we have a _________________________________.
Discrete Random Variables and Their Probability Distributions
A discrete random variable X takes a ________________________________________________
__________________________________________. The probability distribution of a discrete
random variable X lists the ____________ and their ___________________________.
Value of X
x1
x2
x3
...
xn
Probability
p1
p2
p3
...
pn
The probability must satisfy two requirements:
1) ___________________________________________________________________________
2) ___________________________________________________________________________
12) Read through the example on page 343 - 344 (Apgar’s Scores: Babies’ Health at Birth).
Note that the probability of _____________________________________________________________
___________________________________________________________________________________.
*When working with discrete random variables, those probabilities will be different. But with
continuous random variables, these probabilities will be the same. (Just keep this in mind –
sometimes it is easy to mix up when the “equal to” makes a difference.
13) Complete the following problem:
The instructor of a large class gives 26% of the student’s A’s, 42% B’s, 20% C’s, 10% D’s, and
2% F’s. Choose a student at random. The student’s grade on a four-point scale is as followed:
They receive a 4 if they get an A, B = 3, C = 2, D = 1, and F = 0. Therefore, X is discrete random
variable.
a. Construct a probability distribute for this discrete random variable.
b. Write the event “the student received a grade of 3 or 4” in symbols in terms of the random
variable X. What is the probability of the event? Say in words what it means.
c. Write the event “the student got a grade worse than a C” in symbols in terms of the
random variable X. What is the probability of the event? Say in words what it means.
d. Sketch a graph of the probability distribution. Describe what you see.