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Unformatted text preview: ECON 103, Lecture 2: Statistics Review Maria Casanova April 2nd (version 2) Maria Casanova Lecture 2 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 (countable infinite) 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: height of an individual at UCLA Maria Casanova Lecture 2 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 , x 2 ,..., x p is defined as: f ( x ) = Pr ( X = x j ) for j=1,...,p for X = x j 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 .25 .5 .75 1 0 = tails 1 = heads (a) probability distribution .25 .5 .75 1 0 = tails 1 = heads (b) CDF Maria Casanova Lecture 2 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 density function between any two points is the probability that the random variable falls within two points....
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 Spring '07
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