1 Random Variables: Averaging polls Polling rms do lots of statistical modeling to improve the quality of their estimates. As in most modeling problems, they face a bias / variance tradeoff: the harder they try to adjust for all the different biases in their data, the more they will inate the variance. Suppose there are n polling rms each carrying out their own poll to estimate who intend to vote for the Republican candidate in a certain election. We therefore observe n random variables, X1, . . . ,Xn. Each X,- is a result of the ith rm's poll indicating the proportion of voters who intend to vote for the Republican candidate, expressed in percentage points (i.e. 0 g X, g 100 for all X,). The true percentage is some number 6, with 0 S 6 S 100. Due to factors like the sample size of each poll, the non-response bias, and the particularities of each rm's polling methodology, the random variable X,- has mean ,u, and variance of. Assume that the polls are independent. The true percentage is 9, which may or may not be equal to any of the u,- values. (d) (2 points) Some polls may be higher quality than others, so we might want to give them more weight. Assume instead we are going to calculate a weighted average A I i wiXi, i:1 where the weights sum up to 1 (217% : 1). What are the bias, variance, and MSE of A