1. M

    uniform acceleration

    A car, starting from rest and travelling from p to q on a straight level road, where | pq | = 10 000 m, reaches its maximum speed 25 m/s by constant acceleration in the first 500 m and continues at this maximum speed for the rest of the journey. A second car, starting from rest and travelling...
  2. I

    Uniform quantizer with normal distribution input

    A signal that has amplitudes with zero mean and unit variance is applied to a quantizer that is a 8 level uniform quantizer with levels -3.5*d, -2.5*d .... 3.5*d, pick d so that the probability X falls outside th range of the quantizer is 1%My approach to this problem was to use a q function...
  3. I

    Function of uniform random variable.

    Hello this is the problem I'm working on. a voltage X is uniformly distributed in the set {-3,-2,-1,0,1,2,3,4} A. Find the pdf and CDF of the random variable X. for this question I found the pdf as [[pdf=1/7 for -3<=X<=4 and 0 else]] also I found the CDF as [[ CDF= (X+3)/7 for...
  4. Vinod

    Discrete Uniform Distribution: Hypergeometric Model

    Hi members, Suppose that a population consists of m objects; r of the objects are type 1 and m−r are type 0. Thus, the population is dichotomous.A sample of n objects are chosen at random without replacement from the population. Let $X_i$ denote the type of the ith object chosen,for $i \in...
  5. Y

    uniform distribution mle

    xi(i=1,2,...n) is random sample of uniform distribution when a<x<b what is the mle? i know the answer a=minXi b=maxXi in min xi and max xi i is equal value? for example minx3 maxx3 (i=3) plus why answer is min xi max xi
  6. Z

    disproving uniform convergence

    Hello I was given a task to investigate the uniform convergence of the attached series on the real line (in a fourier analyis course) From what I have seen at wolfeam alpha, it does not converge uniformly on R. How can I prove it?
  7. I

    uniform continuity at sinx

    How can I prove that this function is not uniform continuous at R \mathop {\sin (e}\nolimits^x ) I dont know how to solve this . even how to begin. I didnt learn l'hopital rule yet.
  8. H

    How to evaluate surface area & volume of a uniform tetradecahedron

    A uniform tetradecahedron has 2 congruent regular hexagonal faces each with side a=20 cm & 12 congruent trapezoidal faces. All its 18 vertices eventually & exactly lie on a spherical surface with a certain radius. How to evaluate the surface area & volume of solid. any help is greatly...
  9. Vinod

    Approximation of uniform distribution

    Hi members, Fifty numbers are rounded off to the nearest integer and then summed.If the individual round-off errors are uniformly distributed over (-0.5,0.5)approximate the probabilitythat the resultant sum differs from the exact sum by more than 3 ANSWER:- If we let $X_i$ denote individual...
  10. M

    Expectation of 1/Y for Uniform

    Hi, I need to find the expection of 1/Y where Y is distributed by UNIF(1,2). Can I do a jacobian transformation to find the pdf of 1/Y and then \int(1/Y)f_{1/Y}(Y) with limits 1 and 2? Help much appreciated
  11. M

    Uniform Minumum Variance Unbiased Estimator

    Does anyone know how to deduce a UMVUE of a uniform distribution with parameters (-a/2, a/2). I found the MLE of a which simply would be max(-2x1:n,2xn:n). Im not sure if I'd use CLRB to get the UMVUE, when I tried to use CLRB I got (n2/a2) as my answer. Thanks
  12. B

    Uniform Prob. Distribution problem.

    Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. f(x) I found out to be .05 120<= x <= 140 ( converted the hours into...
  13. F

    Probability that sample mean is greater/less than... (CLT, discrete uniform dist)

    Hey mathhelpforum! I'm stuck on a rather simple exercise from Applied statistics and probabilities for engineers, 4th edi. it is exercise 7.9. the solution is supposed to be 0,2312. I try to use the formula Z = (Sample mean - mean) / ((standard deviation)*n^(1/2)), so for the first limit...
  14. D

    Help understanding a proof (Uniform Convergence)

    The lecturer proved a theorem in class, however I have found a step that he did redundant. But maybe I don't understand what he tried to do there. I uploaded the file. (The subject is Uniform convergece) Appreciate if someone can tell me why he did what he did.Thanks!!
  15. U

    Uniform convergence and boundedness

    Assume that $(f_n)$ is a sequence of continuous functions on $[a,b]$, which converge uniformly. Prove that $(f_n)$ is uniformly bounded, i.e., there exists $M \ge 0$ such that, for any $n \in \mathbb{N}$ and any $x \in [a,b]$, $|f_n(x)| \le M$. Here is my attempt, I used the definition of...
  16. A

    Unbiased Estimators - Uniform Distribution

    Let Y1, Y2, ... Yn denote a random sample from uniform distribution on the interval (0, theta) ... let YBAR = sample mean, MAX = sample maximum Consider: estimator1 = 2(YBAR) estimator2 = ([n+1]/n)MAX Show that both estimators are unbiased estimators of theta. Find the efficiency of...
  17. Y

    Uniform convergence of sequence of functions

    Let {an},{bn}, {cn} be three sequence converges to a, b, c respectively. (a) Let B > 0 be a real number. Let fn(x) = an + bnx + cnx2. Show that {fn} converges uniformly to f(x) = a + bx + cx2 on [-B,B]. (b) Prove or disprove that {fn} converges uniformly to f(x) on R.
  18. A

    Statistics - Uniform Distribution

    Let X1, X2, ... Xn be independent, uniformly distributed random variables on the interval [0, theta]. a.) Find the c.d.f. of Yn = max(X1, X2, ..., Xn). b.) Find the p.d.f. of Yn = max(X1, X2, ..., Xn). c.) Find the mean and variance of Yn = max(X1, X2, ..., Xn). d.) Suppose that the number...
  19. M

    Proving Uniform Convergence with epsilon proof.

    Prove that fn(x) = n2x2e-nx converges uniformly on [1, inf). I have to use epsilon proof. I have found the point-wise limit f(x) = 0. I let e > 0. So far I have bounded n2x2e-nx < n2x2e-n. I can't seem to eliminate this x2. Any hints? Thanks.
  20. H

    Uniform Continuity and Continuity

    Let S be the set of points on an interval and let f be continuous on S. Then at every point x there is a neighborhood of x st |f(x)-f(y)|<ε if |x-y|<δ(x). The set of all δ(x) form an open cover of S. If S is compact, (closed and bounded, [a,b]), then there is a finite collection of the...