Time Series Plot:
a simple graph of data collected over time that can be invaluable in identifying trends
or patterns that might be of interest.
Life Expectancy over Time
Year
Life Expectancy over Time
194
0
62.9
195
0
68.2
196
0
69.7
197
0
70.8
198
0
73.7
199
0
75.4
200
0
76.9
2000.00
1990.00
1980.00
1970.00
1960.00
1950.00
1940.00
year
75.00
70.00
65.00
life_expectancy
5.1 How Can Probability Quantify Randomness?
Random phenomenon
– We cannot predict the next outcome, but a regular and predictable pattern
emerges in the long run.
This pattern follows the laws of probability.
Random does NOT mean
haphazard – it is a kind of order that emerges in the long run.
Example:
Studying the concept of probability when tossing a fair coin.
a)
What is the probability of getting a head if we toss a fair coin?
b)
Flip the coin once.
What is the result?
Tails or Heads? ______________ Proportion of heads
obtained in all your tosses so far: ______________
Is this close to the probability of heads you
expected?
Why?
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Flip the coin nine more times.
What are the results? _______________________
Proportion of heads obtained in all your tosses so far: _______________ Is this close to the
probability of heads you expected? ______Why?
d)
Imagine flipping the coin a thousand times.
What will the results be? ______________________
Should the proportion of heads obtained in all your tosses be closer to the probability of heads you
expected? Why? ___________________________________
Probability Quantifies LongRun Randomness
Probability of an outcome of a random phenomenon is the proportion of times the outcome would occur
in a very long series of independent trials.
Probability is a longterm relative frequency.
Computer
simulations are useful for “pretending” we are performing an experiment a very large number of times.
Independent trials:
the outcome of any one trial is not affected by the outcome of any other.
Why do we need probability?
Probability is used to describe games of chance, the flow of traffic
through a highway or the Internet, the spread of diseases or rumors, the rate of return of investments, etc.
5.2 How Can We Find Probabilities?
Probability of an event E:
denoted P(E),
number of outcomes favorable to E
P(E)
number of outcomes in the sample space
=
Note:
This method for calculating probabilities is appropriate only when the outcomes of an experiment
are equally likely.
Rolling Dice:
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 Fall '07
 Ruffin
 Probability, Probability theory, Total College High School Elementary

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