# uniform

1. ### 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. ### 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. ### 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...

16. ### 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. ### 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. ### 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. ### 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. ### 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...