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Next: Exercise 6.2 Up: No Title Previous: Exercise 5.3

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.



2000-08-26