[b]1. Let X1,...,Xn be iid with cdf Fθ, where Fθ(x) = (x/θ)^β for x in [0, θ]. Here β>0 is a known constant and θ>0 is an unknown parameter. Let X(n)= max (X1,...,Xn). f(x|θ)=nβ(x^(nβ-1))/(θ^(nβ)) when x is in [0, θ].
Part one was to show that P= X(n)/θ is a pivot for θ. Which I did by...
Alright, I think I got the first part of the proof. Now to show that the quotient group isn't cyclic, the back of my book says to observe that it has 2 subgroups of order 2... I'm not seeing what these 2 subgroups are, maybe just because quotients groups confuse me.
1. Suppose that H and K are distinct subgroups of G of index 2. Prove that H intersect K is a normal subgroup of G of index 4 and that G/(H intersect K) is not cyclic.
2. Homework Equations - the back of my book says to use the Second Isomorphism Theorem for the first part which is... If K...