Question 6.136

6.136 Sample mean distribution.

Consider the following distribution for a discrete random variable :

−2 −1 0 1
1/4 1/4 1/4 1/4

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

  1. Hand draw the probability distribution of .
  2. Find on either of the trials.
  3. Find the probability that is less than 0 for both trials.
  4. List out all the possible outcomes of the experiment. Find all the possible values of , and determine the probability distribution for the possible sample mean values.
  5. Based on the probabilities found in part (d), hand draw the probability distribution for the sample mean statistic. Describe the shape of this probability distribution in relationship to the probability distribution of part (a). What phenomenon discussed in this chapter is taking place?
  6. Find the probability that the sample mean statistic is less 0. Explain why this probability is not the same as what you found in part (c).