Recent content by dim&dimmer

ok, Z/mZ is a cyclic group (iso to Z mod(m)) with order m, and Z/nZ has order n. Isomorphism preserves orders so ker(g) = mnZ iff m and n are coprime, so that the order of Z/mZ x Z/nZ is mn. Does this complete the proof

Attempt 1: Define g : Z --> Z/mZ x Z/nZ, z |---> (z (mod m), z (mod(n)) Since domain and range are abelian g is a homomorphism as g(ab) = (a+b mod(m), a+b mod(n)) = (a mod(m), a mod(n)) + (b mod(m), b mod(n)) = g(a) + g(b) ker (g) = mnZ ,as n(m.z mod(m)) = n.0 = 0 g is onto. I think this is...

Well, I am none the wiser, you'll have to dumb it down for me, for g(i) does i represent the identity or neutral element, would g(i) = (0,0) ? Still lost

Ok, this sounds good but I haven't got a clue about how to start doing it. Would the isomorphism then end up looking something like f : Z/ker(g) ---> Z/mZ x Z/nZ ==> f : Z/mnZ --> Z/mZ x Z/nZ (as ker(g) = mnZ) Any tips on constructing the hom g:Z -->Z/mZ xZ/nZ would be appreciated, I've...

Homework Statement Show that Z/mZ X Z/nZ isomorphic to Z/mnZ iff m and n are relatively prime. (Using first isomorphism theorem) Homework Equations The Attempt at a Solution Okay, first I want to construct a hom f : Z/mZ X Z/nZ ---> Z/mnZ I have f(1,0).m = 0(mod mn) =...

Homework Statement Let X ~ P (lambda_x) , Y ~ P (lambda_y) X<Y independent. Use change of variable technique to show that, X + Y ~ P (lambda_x + lambda_y) Verify your result using MGFs. Homework Equations The Attempt at a Solution Really struggling! Started...

Ok, I understand this and also can reason that the probability would be very high, just by thinking of the graphs of the distributions, however I am still at a loss as to how to compute the probability. I use R to do the calculations, is it some kind of t test or do I put in the distributions...

t distribution?? Homework Statement If U and V are independent, U being distributed N(3,16) and V being distributed as chi-square on 9 degrees of freedom, find P(U-3 < 4.33 sqrtV). Homework Equations The Attempt at a Solution Well I don't even know where to start! Does U-3...

Homework Statement rvX has f(x) = \alpha \exp^{-\alpha x} , and \ W = 2n \alpha \overline {X} defines a random sample from the distribution. Use moment generating function techniques to show that the distribution of W is chi-square on 2n degrees of freedom. Homework Equations The Attempt...

Thank you, Sheesh, should have posted my question ...days ago, pretty simple really. Dimmer.

Homework Statement W = \frac{vS^2}{\sigma^2}, distributed as X^2_v Find E(s^2) and Var(s^2) Homework Equations E(W) = v , Var(w)=2vThe Attempt at a Solution Have been trying to figure this out with no luck. Can I use MLE for variance to show Var(s^2)= \sigma^2? Really don't know how to get...

Homework Statement Show that the nxn matrix A is invertible iff its determinant is non-zero. I think I can do this, but would like the validity checked. Homework Equations I would use |A| = the product of diagonal entries, because I don't know how to prove the non-diagonal entries of zero...

so... B matrix is \left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] is the domain? codomain of B is \left[\begin{array}{ccc}0 & 1 & 0 \\ 0 & 0 & 2 \\ 0 & 0 & 0\end{array}\right] as you said B' domain is \left[\begin{array}{ccc}1 & 1 & 1 \\ 0 & -1 & -1 \\ 0 & 0...

[/b]1. Homework Statement [/b] Let P_2 be the set of all real polynomials of degree no greater than 2. Show that both B:={1, t, t^2} and B':= {1, 1-t, 1-t-t^2} are bases for P_2. If we regard a polynomial p as defining a function R --> R, x |--> p(x), then p is differentiable, and D: P_2 -->...

I have figured it out