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# powerthree - Econ 240A Power Three 1 Summary Week One...

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1 Econ 240A Power Three

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2 Summary: Week One Descriptive Statistics measures of central tendency measures of dispersion Distributions of observation values Histograms: frequency(number) Vs. value Exploratory data Analysis stem and leaf diagram box and whiskers diagram
3 Probability The Gambler Kenny Rogers 20 Great Years

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4 Outline Why study probability? Random Experiments and Elementary Outcomes Notion of a fair game Properties of probabilities Combining elementary outcomes into events probability statements probability trees
5 Outline continued conditional probability independence of two events

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6 Perspectives About Probability Logical Discipline (like economics) Axiomatic: conclusions follow from assumptions Easier to Understand with Examples I will use words, symbols and pictures Test Your Understanding By Working Problems
7 Why study probability? Understand the concept behind a random sample and why sampling is important independence of two or more events understand a Bernoulli event example; flipping a coin understand an experiment or a sequence of independent Bernoulli trials

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8 Cont. Understand the derivation of the binomial distribution, i.e. the distribution of the number of successes, k, in n Bernoulli trials understand the normal distribution as a continuous approximation to the discrete binomial understand the likelihood function, i.e. the probability of a random sample of observations
9 Uncertainty in Life Demography Death rates Marriage divorce

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10 Uncertainty in Life: US (CDC)
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12 Probability of First Marriage by Age, Women: US (CDC)
13 Cohabitation: The Path to Marriage?: US(CDC)

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14 Race/ethnicity Affects Duration of First Marriage
15 Concepts Random experiments Elementary outcomes example: flipping a coin is a random experiment the elementary outcomes are heads, tails example: throwing a die is a random experiment the elementary outcomes are one, two, three, four, five, six

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16 Axiomatic Basis or Concepts Elementary outcomes have non-negative probabilities: P(H)>=0, P(T)>=0 The sum of the probabilities over all elementary outcomes equals one: P(H) + P(T) = 1 H H T Flip a coin
17 Axiomatic Basis or Concepts II The probability of two mutually exculsive events is zero: P(H and

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powerthree - Econ 240A Power Three 1 Summary Week One...

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