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  1. B

    Probablity question (confused on the pdf)

    Homework Statement [itex] $f(x)=\begin{cases} 7(4)^{-i} & x\in(\frac{1}{2^{i}},\frac{1}{2^{i-1}}],i=1,2,3,...\\ 0 & 0\geq x,x>1 \end{cases}$ (please excuse the poor latex) Homework Equations The Attempt at a Solution the problem i'm having is say x=3/4. then according to the pdf...
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    Basic stats question involving borel sets

    Homework Statement http://i.imgur.com/tjpka.png (the actual problem is the third part down) Homework Equations the first two parts are the definition of borel sets,and the second part is a relevant theorem. The Attempt at a Solution so I'm new to Borel sets. And I feel like I'm...
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    Can you use induction on n cases (as opposed to infinity)?

    Homework Statement this is probably a dumb question, but i'm doing this proof where i have to show two sets are equal, where each set is a union from 1 to n sets. this is pretty easy to show with induction, i think, but i'm used to using induction when i have an infinite amount of things, so...
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    A little help understanding this bayesian problem (very basic)

    Homework Statement so i'm trying to teach myself bayes, and i got a book, and i'm going through trying to do the exercises, and lo and behold, i get stuck on the first one. i thought i was getting it, but the answer given at the back of the book is different than mine. Homework...
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    R or bayes for independent study?

    i'm an undergrad in stats, and next semester is my last. i'm doing an independent study next semester, and am unsure of what would be more beneficial for me: a class in R, or bayes. i would like to do bayes, and i'm decent on computers with limited programming experience, so i'm not too worried...
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    Sequences in complex (just a clarifying question)

    Homework Statement (excuse lack of latex) show that if SUM(zn)= S and SUM(wn= T, then SUM(zn + wn) = S + T Homework Equations The Attempt at a Solution so if i'm doing this right, this is pretty easy, i think. they want me to use a theorem that says if zn=xn +iyn, and SUM(zn)= S, where S...
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    Need help understanding how to interpret a statistics problem

    Homework Statement Let c be a constant, and define Y_{i}=1 if X_{i}\leq c and zero otherwise. Find a statistic that is a function of Y_{1},Y_{2},...Y_{n} and also unbiased for F_{X}(c)=\Phi\left(\dfrac{c-\mu}{\sigma}\right). Homework Equations The Attempt at a Solution not even...
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    Stats: figuring out ranges of transformed variables

    Homework Statement so in general, i am having difficulty in figuring out the range of a transformed variable. sometimes it's easy, i just plug in values and get the other values out, but sometimes i'm not seeing it. for example: f(x)=4x3, for 0<x<1 and let U = (X-.5)2. Finding the pdf of U...
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    Finding a combination discrete and continuous cdf to make a new cdf

    Homework Statement Let F(x)=\begin{cases} .25e^{x} & -\infty<x<0\\ .5 & 0\leq x\leq1\\ 1-e^{-x} & 1<x<\infty\end{cases}$. Find a CDF of discrete type, F_d(x) and of continuous type, F_c(x) and a number 0<a<1 such that F(x)=aF_d(x)+(1-a)F_c(x) Homework Equations The Attempt at a...
  10. B

    Transforming a uniform distribution into a binomial

    Homework Statement Let X~UNIF(0,1). Find y = G(u) such that Y = G(U)~BIN(3,1/2) Homework Equations The Attempt at a Solution after a bit of searching/reading, i found how to do this with a continuous distribution (the problem i had was an exponential, so i took the inverse)...
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    Having a little trouble with functions of random variables

    Homework Statement Let X ~UNIF(0,1), and Y=1-e-x. Find the PDF of Y Homework Equations The Attempt at a Solution So i have Fy=Pr(Y<y) =Pr(1-e-x<y) =Pr(-e-x<y-1) =Pr(e-x>1-y) =Pr(-x>ln(1-y)...
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    Uniform convergence (need help understanding how to apply a theorem)

    Homework Statement show a function f_n is not uniformly convergent using a theorem: Homework Equations if f_n converges uniformly to F on D and if each f_n is cont. on D, then F is cont. on D The Attempt at a Solution not really sure what to do. use the contrapositive? would that...
  13. B

    Could someone take a look at an analysis proof?

    Homework Statement first off, my latex isn't coming out just right. i've attached a pdf that should look right. if you can fill in the gaps from what i've posted here, sweet, otherwise, if you wouldn't mind checking out the attached pdf, that would be awesome. Assume that...
  14. B

    Stats: mle with two parameters

    Homework Statement in a genetics situation, we have two variables, x1 and x2, such that both x1 and x2 >0, and x1+x2<1. we have: p1 = x12 p2 = x22 p3 = (1-x1-x2)2 p4 = 2x1x2 p5 = 2x1(1-x1-x2) p6 = 2x2(1-x1-x2) find the mles for x1 and x2. Homework Equations the answer (from the...
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    Unbiased estimator for exponential dist.

    Homework Statement let X1, X2,... Xn form a random sample of size n from the exponential distribution whose pdf if f(x|B) = Be-Bx for x>0 and B>0. Find an unbiased estimator of B. Homework Equations The Attempt at a Solution nothing yet. i don't really know where to get started. a...
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    Statistics and AI

    so, my dream job is work on the math end of artificial intelligence. i don't know how much of an option that is for me. i will be getting my undergrad degree in math with a stats minor here pretty soon, but i'm debating on getting a double major in stats and going on to grad school. does anyone...
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    Probability (involving conditioning)

    Homework Statement a deck of cards is shuffled and then divided into two halves of 26 cards each. a card is drawn from one of the halves; it turns out to be an ace. the ace is then placed in the second half-deck. the half is then shuffled, and a card is drawn from it. compute the probability...
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    Please check my proof (generalized eigenspaces)

    Homework Statement let T be a linear operator on V, and let λ be an eigenvalue of T. prove that if rank((T-λI)m = rank((T-λI)m+1 for some integer m, then Kλ = N((T-λI)m. Homework Equations this is part 4 of a 6 part proof, and in the earlier stages, i showed if rank((T-λI)m =...
  19. B

    Linear - from a charpoly, determine if T is one to one, and nullity T

    Homework Statement if T is a linear operator on V and dim V = 4 and charpoly(T)=t2(t-1)(t+7), then is T one-to-one? What is the dimension of the nullspace of T? Homework Equations The Attempt at a Solution So i know T has 3 eigenvalues, 0, 1, -7. Since 0 is an eigenvalue, i know...
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    Solved, i think (S is linearly indep. iff every finite ss of S is linearly indep.

    Homework Statement S is linearly independent iff every finite subset of S is linearly independent. Homework Equations The Attempt at a Solution letting S be linearly independent is pretty easy. i am slightly worried about my logic for the other way though. it goes like this...
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    Probability: sampling without replacement

    Homework Statement there are 30 red balls, 30 white balls, and 30 blue balls in a container. you draw 10 of them, without replacement. what is the probability that at least one color won't be selected. Homework Equations The Attempt at a Solution i've been working on this one for...
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    How important was einstein, really?

    i've heard several teachers talk about ideas being ripe at certain times, and while we often attribute amazing progress to certain individuals, really, the scientific community at large was pretty close to the results. newton/leibniz, for example. one teacher talked about how archimedes was...
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    A little help with a binomial theorem proof

    Homework Statement (here, (n,k) reads n choose k) prove that (n,0) - (n, 1) + ... + (-1)n(n,n) = 0 Homework Equations binomial theorem The Attempt at a Solution so this proof is relatively straightforward when n is odd. it's just matching up terms and having them cancel each other...
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    Math Careers for math majors

    i've been kind of slow going through college. the last time i met with a counselor, i found i was about a year away from a bachelor's in general math, so i decided to focus on that. later, i asked a teacher what people do with a degree in general math. she said that usually people studying...
  25. B

    Please check my proof of sum of n choose k = 2^n

    Homework Statement (here (n,k) reads n choose k)(and again, please excuse that i don't use latex) claim: (n,0) + (n,1) + (n,2) + ... (n,n) = 2n Homework Equations binomial theorem The Attempt at a Solution proof: sum(k=0 to n of (n,k)) = sum(k=0 to n of (n,k))*1k*1n-k. by the...
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    A little help with a beginning stats proof

    Homework Statement Let A_1, A_2... be any infinite sequence of events, and let B_1, B_2... be another infinite sequence defined as B_1=A_1, B_2=A_1cA_2, B_3=A_1cA_2cA_3 and so on. Prove that Pr(Union i=1 to n A_i) = Sum i=1 to n Pr(B_i). (sorry if that notation is hard to understand)...
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    Looking for a hint on a stats proof

    so i'm somewhat new to statistics proofs, but this one is for the most part a sets proof, which i can do. i'm having trouble connecting them. (c = complement)(AB = A intersect B) Let A_1, A_2... be any infinite sequence of events, and let B_1, B_2... be another infinite sequence defined as...
  28. B

    Inner automorphisms (need clarification)

    Homework Statement Show that the inner automorphisms of a group G form a normal subgroup of the group of all automorphisms of G under function composition. Homework Equations in the previous problem, i showed that all automorphisms of a group G form a group under function composition...
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    Math Teaching vs something else (math degree)

    so i'm pretty close to getting a bachelor's in general math. but i kind of want to teach as well. part of me wants to teach for a few reasons: one, the selfish reason, is that when you teach, you really understand the stuff, and i know a lot of stuff as fact, not really as understanding...
  30. B

    Properties of the internal direct product of subgroups

    Homework Statement Let H and K be groups and let G = H x K. Recall that both H and K appear as subgroups of G in a natural way. Show that these subgroups H (actually H x {e}) and K (actually {e} x K) have the following properties: a: every element of G is of the form hk for some h in H and k...
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