1. Showthat S(y,- — y) must equal 0 for any collection of observations yi,y2^ • - >y«- 2. The Russian mathematician Tchebysheff proved that for any A: > 1, the proportion of observations that fall...

1. Showthat S(y,- — y) must equal 0 for any collection of observations yi,y2^ • - >y«-

2. The Russian mathematician Tchebysheff proved that for any A: > 1, the proportion of observations that fall more than k standard deviations from the mean can be no greater than \/k~. This holds for any distribution, notjust bell-shaped ones,

(a) Find the upper bound for the proportion of observationsfalling(i) more than two standard deviations from the mean, (ii) more than threestandard deviations from the mean, (iii) more than ten standard deviations from the mean,

(b) Compare the upper bound for A: = 2 to the approximate proportion falling more than two standard deviations from the mean in a bell-shaped distribution. Why is there a difference?