Recent content by missavvy

It would be Ʃ (E(Xi) - μ) = 0 ? How would I calculate E(1/2θ3) ? (I know I wouldn't need to here since it's 0 on top, but just out of curiosity)

Homework Statement I am just trying to figure out how to calculate the expectation of something. The context is for a random sample from a normal distribution with known mean μ and unknown variance σ2. Homework Equations 3. The solution So for the purposes of this question we set θ = σ2 I...

I'm just give that f is continuous... I'm not told that any set U is open though, so I don't know if I can use that definition. Is there a way to do this using a delta epsilon definition? Or neighbourhoods?

Ok.. So to clarify, we have points in MxN, (m,n) , n not in f(M) (m,n') not in graph(f) Then do I use the defn of continuity on these two sets of points?

hm, I am not sure I understand.. so if I take points in MxN, that are not in the graph, then we have (x,f(x)) but x is not in M, which wouldn't make sense, would it?

Homework Statement Let M, N be two metric spaces. For f: M --> N, define the function on M, graph(f) = {(x,f(x)) \inMxN: x\inM} show f continuous => graph(f) is closed in MxN Homework Equations The Attempt at a Solution I can't figure out what method to use. I have...

Homework Statement Let M be a metric space, A a subset of M, x a point in M. Define the metric of x to A by d(x,A) = inf d(x,y), y in A For \epsilon>0, define the sets D(A,\epsilon) = {x in M : d(x,A)<\epsilon} N(A,\epsilon) = {x in M: d(x,A)\leq\epsilon} Show that A is...

um, can i just say since R is complete, i can find for any sequence xn in R+, an x s/t lim xn = x... and th rest follows?

Hm, ok.. I noticed the rewrite you mentioned, and attempted to do something with it to somehow get a lovely conclusion but I'm not sure what it is. I have | ln(xj) - ln(xi) |, what i need is something greater than or equal to that.. i first thought of the triangle inequality but i don't know...

Homework Statement Given (R+, d), R-Real # d= | ln(x/y) | Show that this metric space is complete Homework Equations The Attempt at a Solution Firstly, I know that to show it is complete I need to have that all Cauchy sequences in that space converge... So I'm not 100%...

ok .. so I get up to his point: \int (FROM 0 to 1) (2\pir2(-cos\varphi)) (from 0,tan-1(1/2) ) dr (I may have used different variables than what you suggested, but basically I get that) How can I sub in the tan into the phi ? do I evaluate arctan(1/2) then put it into the CosPhi? it`s a messy...

Homework Statement If A=<1+i> in Z[i], show that Z[i]/A is a finite field and find its order Homework Equations The Attempt at a Solution Not sure where to start... Z[i]/A = {m+ni + A, m, n integers} ? is that right? And I don't know what else to do.

Homework Statement Find the volume of the cone bounded below by z=2root(x2+y2) and above by x2 + y2 + z2 = 1 Homework Equations The Attempt at a Solution Ok I have the solution, I just don't understand how to get it! So I know I have to change into spherical coordinates but...

Ok, I think I got it.. I'm working on b), where h(x)= x^2 for the units: So then elements are of the form {ax+b: a,b in F, x^2 =0} Not sure if it's right, but I took (ax+b)(cx+d) = 1 and expanded to get axd + bcx + bd = 1 Then (ad + cb)x=0 and bd = 1 So b=d=1 or b=d=-1 -> a=-c Err, am I...

So I get (ax+b)(ax+b) = a2x2 + 2bax + b2 = ax+b and since x2 = x here, then a2x + 2bax + b2 = ax + b Whats the best way to factor this? I have ba together so I'm not sure. I tried ax(a+ 2b -1) = b-b^2.. I got 0,1 as idempotents... ...sometimes it's the simple things that end up...