A hint to get started
Keep the square-root growth in the large-sample tail
, with mean 3 and variance 4. S sums 100 independent observations of X; T sums a further 300 independent observations. Give numerical answers to 3 decimal places.
(i) Find .
(ii) Find .
(iii) N sums n independent observations of X. State the approximate value of as n becomes very large, with justification.
[1989/II/9]
CJC · Discussion · Question 13
The gap from the mean grows like n, while the sum’s standard deviation grows like√n.