[gov2001-l] pset 2

Hi all, Problem set 2 has been graded and will be handed back to you Monday after class. Those who only submitted online already have your grades and comments posted in the dropbox. Just a few things that generally people need to pay attention to: 1. Probabilities are always between 0 and 1. 0.3 is a probability. 30% is not a probability. 2. While one estimator can be more biased than another, there is no such thing as "less unbiased". All unbiased estimators are unbiased the same amount. There is no degree to the unbiasedness. 3. On that same note, a few people wrote that the midrange and mean estimators were slightly biased for the uniform and normal distributions because the means were slightly off. This is not true. The expectation of both estimators is equal to the population mean. The "bias" that you see is purely from simulation error (if we had infinite number of simulations, the mean of the sampling distribution would be exactly the population mean). 4. It's generally not a good idea to name objects in R the wrong names. A few of you named E(X^2) as "var", which is not true. It is a component of variance, but not the actual variance, so naming it wrong can be confusing. 5. For 4d, while it is great that many of you wrote functions for the random variable Y, it is not necessary. You can just do the operations on the X draws themselves. 6. When you are trying to compare quantities via two graphs, it is usually a good idea to have the graphs on the same scale for ease of comparison. If the Y axes are different, it makes it harder to actually compare whether the spreads are smaller/bigger, etc. -- Patrick Lam Department of Government and Institute for Quantitative Social Science, Harvard University http://www.people.fas.harvard.edu/~plam