1. By definition, a random variable, , needs to have a numerical outcome. Generate a new data series of outcomes, , corresponding the analysts recommendations as follows: =3.0 if recommendation is STRONG BUY =2.5 if recommendation is BUY =2.0 if recommendation is HOLD =1.5 if recommendation is UNDERPERFORM =1.0 if recommendation is SELL

B. Assume that the analysts recommendations in the data set are a random sample drawn from an underlying population of analysts recommendation, . Assume throughout this exercise that has a Normal probability distribution with unknown mean, , and unknown variance, 2.1 Compute an unbiased estimate for and an unbiased estimate for 2. (If you know more than one unbiased estimator for , take the one with the smaller sampling variance.)

C) Denote the sample-average estimate as =1 =1 What is the standard error of , i.e. ()?