Recent content by kimkibun

do you have a better explanation sir?

Homework Statement Show that x=cosx, for some xε(0,∏/2). Homework Equations The Attempt at a Solution Define f(x)=x-cosx, i want to show that for some aε(0,∏/2), limx→af(x)=0. is this correct?

sorry, you're right, i forgot the "disjoint" word. is there any other way (probably, easier) to prove that S is a disconnected set?

Homework Statement Let S={zεℂ: |z|<1 or |z-2|<1}. show that S is not connected.Homework Equations My prof use this definition of disconnected set. Disconnected set - A set S \subseteqℂ is disconnected if S is a union of two disjoint sets A and A' s.t. there exists open sets B and B' with A...

Good day! Im currently reading the book of Steven R. Lay's "Analysis with an Introduction to Proof, 3rd ed.". According to his book, if a subset S of ℝ contains all of its boundary then it is closed. But i find this wrong since if we consider S={xεQ;0≤x≤2}, then it can be shown that S...

Homework Statement suppose that n cylindrical shafts are selected at random from the production of the machine and their diameters and lengths are measured. it is found that N11 have both measurements within the tolerance limits, N12 have satisfactory lengths but unsatisfactory diameters...

but sir, according to the definition of path partition, it should be vertex-disjoint..

sorry if i posted this topic here..let P1 and P2 be a path partition of a graph.is it possible that P1 and P2 to have the same end vertices?

Homework Statement Let X1,X2 be a random sample of size 2, from a normal distribution with mean μ and σ2=1. Let T=t(X1,X2)=X1+X2 be the estimator of μ and l(t;μ)=t-μ be the loss function. Compute risk function R(μ). Homework Equations R(μ)=∫∫(l(t;μ))∏f(xi;μ)dxi The Attempt at a...

thank you so much sir! i really appreciate your efforts! God Bless you!

can you please show me how you get that? the mle for μ that i got is this, (Ʃxi/Ʃσi2)(Ʃ1/σi2) is it possible to find the mle of the parameter σi2?

Why is it that the set A={1/n:n is counting number} is not a closed set? We see that no matter how small our ε is, ε-neighborhood will always contain a point not in A (one reason is that Q* is dense in ℝ), thus, all the elements in A is boundary point, and we know that by definition, if...

i forgot to tell you that the n-observations was drawn out from a normal population..well anyway, is it possible that different variances might affect the maximum likelihood of the mean?

is it possible to estimate all parameters of an n-observation (X1,...Xn) with same mean, μ, but different variances (σ21,σ22,...,σ2n)? if we assume that σ2i are known for all i in {1,...n}, what is the mle of of μ?

here's the link sir http://www.sci.ccny.cuny.edu/~shpil/gworld/problems/probmat.html i agree with you sir when it comes to difficulty. my professor said that its a suicide for a graduating student to choose such topic. well anyway, thank you sir for your reply. btw, i enjoy reading the...