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Class Notes 6

# Class Notes 6 - Time Series Plot a simple graph of data...

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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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c) 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 Long-Run 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 long-term 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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Class Notes 6 - Time Series Plot a simple graph of data...

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