Find the value of the correlation

Question

Discuss the following:

Q1: Joint pdf of a sample maximum and minimum is as below

f(a,b)=n(n-1)[F(b)-F(a)]^n-2 f(a)f(b)

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:

f(a)=(k+1)a^k/c^k+1

Where 0≤ a ≤ c

Q2: Find the general formula for the moment below if n=3, k=1, c=1

E(A^γ₍₁₎A^s_(n))

Find the value of the correlation between the largest and the smallest observation in such a sample