Day One
Discrete Variables



P. 469
P. 475
P. 477
2,3,4
8,9,10
11,12,13,18,20
 Discrete
random variable –
countable number of possible
outcomes
 Continuous
random variable –
takes on all values within an
interval
 Gives
the probability associated
with each possible x value
 Usually
displayed in a table, but
can be displayed with a
histogram or formula
1)
For every possible x value,
0 < P(x) < 1.
2) For all values of x,
S P(x) = 1.

Write out the probability Distribution for
rolling a die once.
x
1
2
3
4
5
6
P(x)

Make a histogram of the resulting uniform
distribution
Suppose you toss 3 coins & record
the number of heads.
The random variable X defined as ...
The number of heads tossed
Create a probability distribution.
X
P(X)
0
.125
1
.375
2
.375
3
.125
Create a probability histogram.
Uniform Distribution
Skewed Distribution
Symmetric Distribution
A spinner can land on any number between o and 1.
Find p(.3<x<.7)
Continuous Uniform Distribution


Students are reluctant to report cheating by other
students. A survey puts this question to an SRS
of 400 undergraduates: “you witness two
students cheating on a quiz. Do you go to the
professor?” Suppose that if we could ask all
undergraduates, 12% would answer “yes.”
The proportion p = .12 is a parameter that
describes the population of all undergraduates.
The proportion p-hat of the sample who answer
“yes” is a statistic. The statistic p-hat is a
random variable

We will see in the next chapter that p-hat is
N(.12, .016). Notice that the mean of the
sampling distribution is the same as the
population parameter. THIS IS HUGE.

What is the probability that the results of the
survey differs by more than two percentage
points?

P(x <.1) + p(x > .14)

1 – p( .1<x<.14)