Download ppt

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts
no text concepts found
Transcript
Section 7.1
Discrete and
Continuous Random
Variables
AP Statistics
www.toddfadoir.com/apstats
Random Variables
A random variable is a variable whose
value is a numerical outcome of a random
phenomenon.
 For example: Flip three coins and let X
represent the number of heads. X is a
random variable.
 We usually use capital letters to denotes
random variables.

AP Statistics, Section 7.1, Part 1
2
Random Variables
A random variable is a variable whose
value is a numerical outcome of a random
phenomenon.
 For example: Flip three coins and let X
represent the number of heads. X is a
random variable.
 The sample space S lists the possible
values of the random variable X

AP Statistics, Section 7.1, Part 1
3
Discrete Random Variable
A discrete random variable X has a
countable number of possible values.
 For example: Flip three coins and let X
represent the number of heads. X is a
discrete random variable.
 We can use a table to show the probability
distribution of a discrete random variable.

AP Statistics, Section 7.1, Part 1
4
Discrete Probability Distribution
Table
Value of X:
x1
x2
x3
…
xn
Probability:
p1
p2
p3
…
pn
AP Statistics, Section 7.1, Part 1
5
Probability Distribution Table:
Number of Heads Flipping 4 Coins
TTTT
TTTH
TTHT
THTT
HTTT
TTHH
THTH
HTTH
HTHT
THHT
HHTT
THHH
HTHH
HHTH
HHHT
HHHH
X
0
1
2
3
4
P(X)
1/16
4/16
6/16
4/16
1/16
AP Statistics, Section 7.1, Part 1
6
Discrete Probability Distributions

Can also be shown using a histogram
AP Statistics, Section 7.1, Part 1
7
AP Statistics, Section 7.1, Part 1
8
What is the average number of
heads?
x  0   1  2   3   4 
1
16
6
16
4
16

0
16


32
16
2
4
16

12
16

12
16

4
16
1
16
4
16
AP Statistics, Section 7.1, Part 1
9
Continuous Random Variable

A continuous random variable X takes
all values in an interval of numbers.
AP Statistics, Section 7.1, Part 1
10
AP Statistics, Section 7.1, Part 1
11
Distribution of Continuous Random
Variable
AP Statistics, Section 7.1, Part 1
12
Distribution of Continuous Random
Variable
The probability distribution of X is
described by a density curve.
 The probability of any event is the area
under the density curve and above the
values of X that make up that event.

AP Statistics, Section 7.1, Part 1
13
Normal distributions as probability
distributions

Suppose X has N(μ,σ) then we can use
our tools to calculate probabilities.
AP Statistics, Section 7.1, Part 1
14
Assignment

Exercises: 7.1 - 7.18
AP Statistics, Section 7.1, Part 1
15
Related documents