sample X1...Xn from the U(alp? Let Y1 and Yn be the samllest and the largest order statistics based on a random sample X1...Xn from the U(alpha, bata)(alpha<bata) distribution.
i) For n = 3 and n = 4, show that the joint p.d.f. of Y1 and Yn is given, respectively, by:
g13(y1,y3)=(3*2)/(bata-alpha)^3(y3-y1), alpha<y1<y3<bata
g14(y1,y4)=(4*3)/(bata-alpha)^4(y4-y1)^2, alpha<y1<y4<bata
ii) Generalize the preceding results and show that: g1n(y1,yn) = (n(n-1))/(bata-alpha)^n(yn-y1)^(n-2) alpha<y1<yn<bata
i) For n = 3 and n = 4, show that the joint p.d.f. of Y1 and Yn is given, respectively, by:
g13(y1,y3)=(3*2)/(bata-alpha)^3(y3-y1), alpha<y1<y3<bata
g14(y1,y4)=(4*3)/(bata-alpha)^4(y4-y1)^2, alpha<y1<y4<bata
ii) Generalize the preceding results and show that: g1n(y1,yn) = (n(n-1))/(bata-alpha)^n(yn-y1)^(n-2) alpha<y1<yn<bata