Let 1,2, 3, … , 30 be a random sample of size 30 from a population distributed with the
following probability density function:
() = {
1
2
−
2, 0 < < ∞
0, ℎ
Suppose that = ∑
30
=1
. Use
i) the moment generating function technique to find the probability distribution function of .
Write down the density function of . (4)
ii) the Central Limit Theorem to compute (40 < < 80). (4)
iii) the Chebychev inequality to find the lower bound of (40 < < 80)
