1-46. The Planet Claire has pink air and some unusual inhabitants. Every citizen of Planet Claire has either one or five pet rocks. You may assume there are equal numbers of
1 rock and 5 rock citizens and the overall population of Planet Claire is in the millions. Compute without a calculator

a. Find the mean pet rock ownership of a citizen of Planet Claire.
b. Find the population variance of the pet rock ownership.

1-47.
NASA has sent a deep space probe to Claire to survey its citizens about pet rock ownership. Space travel is very expensive and the probe only has the capacity to survey two citizens at random on the planet.

There are 4 equally likely outcomes of pet rock ownership the NASA probe could find in its random survey of two citizens. List them.

Calculate a variance for each sample listed in part (a).

1-48.
If NASA were able to send many of these probes what would be the average value for the variance in pet rock ownership?

a. Compare the population variance you found in part (b) of problem 1-46 with the mean of the variances found in the samples. Summarize the bias in variance calculations shown in this example.

b. Now repeat your four variance calculations from part (b) of problem1-47, this time dividing the sum of squared differences by (n-1) or 1
instead of n or 2
This adjustment to the denominator makes each resulting value a sample variance.

c. What is the average of these new sample variances? How does it compare to the population variance in part (b) of problem 1-46?