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5­2 mean, variance, standard deviation, and expectation.notebook
December 04, 2014
OBJECTIVE: Find the mean, variance, standard deviation, and expected value for a discrete random variable.
mean
R
E
C
A
L
L
sum of values
total values
sample
population
1
5­2 mean, variance, standard deviation, and expectation.notebook
December 04, 2014
OBJECTIVE: Find the mean, variance, standard deviation, and expected value for a discrete random variable.
APPLY the concept to probability distribution
values a variable can assume and probability of the values
(by theory or observation)
MEAN
⇒
AVERAGE of the occurrences number of times value occurred
total number of occurrences
2
5­2 mean, variance, standard deviation, and expectation.notebook
December 04, 2014
OBJECTIVE: Find the mean, variance, standard deviation, and expected value for a discrete random variable.
Mean
SUM OF (each possible outcome) x (corresponding probability)
formula
(sum of the products)
3
5­2 mean, variance, standard deviation, and expectation.notebook
December 04, 2014
OBJECTIVE: Find the mean, variance, standard deviation, and expected value for a discrete random variable.
variance
standard deviation
ROUNDING
decimal ­ one more place value than X
RULE
fraction ­ lowest terms
4
5­2 mean, variance, standard deviation, and expectation.notebook
December 04, 2014
OBJECTIVE: Find the mean, variance, standard deviation, and expected value for a discrete random variable.
EXAMPLES
Probability Distribution
X
# def. DVD
Probability P(X)
0
1
2
3
0.9
0.05
0.03
0.02
MEAN
5
5­2 mean, variance, standard deviation, and expectation.notebook
December 04, 2014
OBJECTIVE: Find the mean, variance, standard deviation, and expected value for a discrete random variable.
6
5­2 mean, variance, standard deviation, and expectation.notebook
December 04, 2014
OBJECTIVE: Find the mean, variance, standard deviation, and expected value for a discrete random variable.
7
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