lecture2

# lecture2 - ECON 103 Lecture 2 Statistics Review Maria...

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ECON 103, Lecture 2: Statistics Review Maria Casanova January 12th (version 0) Maria Casanova Lecture 2

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Requirements for this lecture: Chapter 2 of Stock and Watson Maria Casanova Lecture 2
1. Random Variables X is a random variable if it takes different values according to some probability distribution Types of random variables: Discrete random variables Take on a finite or number of values Example: outcome of a coin toss Continuous random variables Take on any value in a real interval Each specific value has zero probability Example: wage of a worker in company ABC. Maria Casanova Lecture 2

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2.1. Univariate Probability Distributions Probability distributions of discrete random variables The probability density function of a discrete random variable that takes on values, say, x 1 and x 2 is defined as: f ( x ) = Pr ( X = x 1 ) Pr ( X = x 2 ) Pr ( X 6 = x 1 and X 6 = x 2 ) = 0 The cumulative distribution function (CDF) is the probability that the random variable is less or equal to a particular value. Maria Casanova Lecture 2
2.1. Univariate Probability Distributions Figure: Probability distributions of discrete random variable 0 .25 .5 .75 1 0 = tails 1 = heads (a) probability distribution 0 .25 .5 .75 1 0 = tails 1 = heads (b) CDF Maria Casanova Lecture 2

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2.1. Univariate Probability Distributions Probability distributions of continuous random variables The cumulative distribution function (CDF) of a continuous variable is the probability that the random variable is less or equal to a particular value. The probability density function (PDF) of a continuous random variable is defined as the derivative of the cumulative distribution function (CDF). The area under the probability
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