Imagine a simple experiment of randomly generating a value for X recording it, and then repeating this process a second time. Recognize that it is possible to get the same result in both trials. Finally, take the average of the two observed values.

a. Manually draw the probability distribution of X.

b. Find P(X < 0) for either of the trials (i.e. observing atleast one trial where X < 0).

c. Find the probability that X < 0 for both trials (i.e. observing X < 0 in both trials).

d. List out all possible outcomes of the experiment. Find all possible values of and determine the probability distribution for the possible sample mean values.

e. Based on the probabilities found in part (d), manually draw the probability distribu- tion distribution for the sample mean statistic. Describe the shape of this probability in relation to the probability distribution of part (a). Which phenomenon discussed in this chapter is taking place?

f. Find the probability that the sample mean statistic is less 0. Explain why this prob- ability is not the same as that found in part (c).