Simulation is being used to study a system whose measure of performance X will be partially determined by the outcome of a certain external factor. This factor has three possible outcomes

(unfavorable, neutral, and favorable) that will occur with equal probability (

1 3

). Because the favorable outcome would greatly increase the spread of possible values of X, this outcome is more critical than the others for estimating the mean and variance of X.

Therefore, a stratified sampling approach has been adopted, with six random observations of the value of X generated under the favorable outcome, three generated under the neutral outcome, and one generated under the unfavorable outcome, as follows:

(a) Develop the resulting estimate of E(X).

(b) Develop the resulting estimate of E(X2 ).