Respond to OTA: Basically the first equation is the joint pdf of a sample maximum and minimum - if I am not wrong - it is just the formula.
The problem is finding the joint pdf from the sample size drawn from the pdf (2nd equation given between the bolded text ). So basically A(1) and A(n)corresponds only to the 2nd equation ( f(a) =(k+1)a^k/c^(k+1) )- hope that helps. Let me know if you need further clarification.....that is the way the question was set and it is really confusing for me. Thanks.
Joint pdf of a sample maximum and minimum is as below
Where a < b
Find the joint pdf of the largest and smallest observations , denoted A(n) and A(1) respectively, in a sample of n drawn from the pdf below:
Where 0≤ a ≤ c
Find the general formula for the moment below if n=3, k=1, c=1
Find the value of the correlation between the largest and the smallest observation in such a sample
Joint probability density functions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.