For Exercises 8.49 to 8.51, see page 437; for 8.52 and 8.53, see pages 439–440; for 8.54 to 8.56, see page 440; for 8.57 to 8.58, see page 444; for 8.59, see page 445; and for 8.60, see page 447.

Question 8.51

8.51 Rules for means and variances.

It is quite easy to verify the mean and standard deviation of the difference .

  1. What are the means and standard deviations of the two sample proportions and ? (Look at the box on page 256 if you need to review this.)
  2. Use the addition rule for means of random variables: what is the mean of ?
  3. The two samples are independent. Use the addition rule for variances of random variables to find the variance of .

8.51

(a) (b) . (c)