Exercise 6.1

1.

Suppose the population has the distribution

      Range   0    1
      Prob.   .3  .7

Let $\bar{X}_3$ be the sample average of a sample of size 3 from this population. Using a tree diagram, show that the distribution of $\bar{X}_3$ is

      Range  0       1/3   2/3   1
      Probs  0.027 0.189 0.441 0.343

2.

Show that the means of the population and the distribution of $\bar{X}_3$ have the same value .7.

3.

Show that the variance of the population in #1 is .21.

4.

Show that the variance of $\bar{X}_3$ in #1 is .07.