Recent content by raynard

Thanks for the reply! I tried the standard method you described, but I see no easy way to find the inverse of f: x -> x^2 + x

Homework Statement Given a random variable X with a known distribution (e.g. a beta distribution), find the distribution of f(X) = X^2 + X The Attempt at a Solution I've tried the normal approaches: the standard transformation theorem; conditioning on X; Laplace transformation, etc...

Could you explain how to do this 'trail and error' ?

I still don't have a clue on how to get further in this problem. This is what I've got so far: assuming there exists a subgroup of order 6, all elements should have order 1, 2, 3 or 6. The identity element is the only one having order 1, so that leaves us with 5 other elements. Now there...

Could you explain me why this is so? (We haven't seen any kind of such a theorem)

Homework Statement True or false: U(\mathbb{Z}_{2007}), . (=group of units) has a subgroup of order 6. Homework Equations We know that the \phi(2007) (= Euler's tolient function) = 1332, which is the amount of elements in U(\mathbb{Z}_{2007}), . The Attempt at a Solution We clearly see...

I understand my error in believing every linair function will result in a homomorphism. However, I don't fully understand how the restriction on a generator (gen2006 = 0) can help in finding function that do result in a morphism. The only possible combination is the trivial solution x |-> x.

I was wondering, if we want to define a morphism from \mathbb{Z}2006 to, let's say \mathbb{Z}3008. Obviously, all linear functions like $ x \rightarrow a\cdot x$ will do, but are there any other functions which can result in a homomorphism?

Hi everybody, I was wondering, is it possible to create a multiway switching circuit with 3 switches, and all of them being standard 3-way ones ? (in other words: is it really necessary to use a 4-way switch instead ?) thanks in advance!