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Unformatted text preview: Random variables Covariance and correlation Sampling Asymptotics Econ 281  Introduction to Applied Econometrics Review  Random variables, sampling and estimation Richard Walker Northwestern University April 3, 2008 Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics 1 Random variables Discrete and continuous Expected value rules 2 Covariance and correlation Covariance and variance rules Correlation 3 Sampling Estimators Unbiasedness and efficiency Estimators of other parameters 4 Asymptotics Probability limits Consistency and plim rules Central limit theorems Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics Preliminary note: you will not need to prove any of the following results in an exam But, you will be using them in the rest of the course; your aim should be to get comfortable with them Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics 1 Random variables Discrete and continuous Expected value rules 2 Covariance and correlation Covariance and variance rules Correlation 3 Sampling Estimators Unbiasedness and efficiency Estimators of other parameters 4 Asymptotics Probability limits Consistency and plim rules Central limit theorems Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics Discrete and continuous 1 Random variables Discrete and continuous Expected value rules 2 Covariance and correlation Covariance and variance rules Correlation 3 Sampling Estimators Unbiasedness and efficiency Estimators of other parameters 4 Asymptotics Probability limits Consistency and plim rules Central limit theorems Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics Discrete and continuous A random variable X is any variable whose value cannot be predicted exactly Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics Discrete and continuous A random variable X is any variable whose value cannot be predicted exactly Can take any one of a specified set of possible values (denoted by little x ) Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics Discrete and continuous A random variable X is any variable whose value cannot be predicted exactly Can take any one of a specified set of possible values (denoted by little x ) The correspondence of probabilities to possible values is known as the probability distribution Econ 281  Introduction to Applied Econometrics Richard Walker Random variables Covariance and correlation Sampling Asymptotics Discrete and continuous Discrete random variables A discrete random variable can take one of a finite set of discrete values Econ 281  Introduction to Applied Econometrics Richard Walker Random variables...
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