Problem Set 2.Rmd

# F r oilexporters subsetfl2war fl2oil 1

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####(f) {r} oilexporters <- subset(fl2$war, fl2$Oil == 1) mean(oilexporters) sd(oilexporters) nonoilexporters <- subset(fl2$war, fl2$Oil == 0) mean(nonoilexporters) sd(nonoilexporters)  The higher standard deviation of the amount of war in oil exporting countries means that there is a higher varience in the data (meaning that the rate of war in such countries is more likely to change if re-sampled). The lower standard deviation of the amount of war in non-oil exporting countries means that there is a lower varience in the the data (meaning that the values are more likely to stay the same if re-sampled). ####(g) {r} mean(fl2$ethfrac) min(fl2$ethfrac) max(fl2$ethfrac) This preview has intentionally blurred sections. Sign up to view the full version. sd(fl2$ethfrac)  The variable ranges from 0 to 1 because it is indicating the percentage of the population that has ethnic factionalization (from 0% to 100%). ####(h) {r} plot(fl2$ethfrac, fl2$war, main = "Relationship between War and Ethnic Factionalization", xlab = "Percentage of Ethnic Factionalization Populatio", ylab = "Number of Wars") abline(lm(fl2$war~fl2$ethfrac), col="red")  There is a positive correlation between the percentage of ethnic factions and wars. As the predicted ethnic factionalization increases, the number of predicted wars increases as well. ### Question 3. Suppose you have a random variable $X$ with expectation $E[X]=u$, and variance given by $s^2$. You then draw multiple observations from the same distribution. That is, you draw X_1, X_2,..,X_n, each a random variable wih expectation $u$ and variance $s^2$. ####(a) The average of these random variables is the mean, E[X] = $u$/n ####(b) SD(x) is the sqrt($s^2$) = s ####(c) $E[\overline{X}]$ is the mean of the sample data ####(d) ($Var(\overline{X})$ is the variance of the sample data.
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