Let Y₁, Y2Yn denote a random sample f size n from a population with a uniform distribution on the interval (0, 8). Let Y(n) = max(Y₁, ₂,..., Yn) and U =(a) Show that U has distribution functionu < 0,FU(u) =u", 0 ≤ u≤ 1,(1,u > 1.The distribution function for Y(n) is G(y) =inor,0 ≤ y ≤ 8, so the distribution function for U is given by F(u) = P(U ≤ u) = P(Y(n)) ≤ 0u = G₁(b) Because the distribution of U does not depend on 8, U is a pivotal quantity. Find a 95% lower confidence bound for 8.[Y(n)]Ou|_ ) - \ ,^,0 ≤ y ≤1.

Given, Y1, Y2,......Yn denote a random sample of size n from a population with a…

Answered: (1)(A). (n)" Let Y₁, Y₂Yn denote a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X and Y are random variables having the sample spaces X = y = {0, 1}. We have the following joint distribution function for X and Y: Fx.y (x, y) = 0.3 if x = 0, y = 0 = 0.1 if r = 1, y = 0 = 0.4 if z = 0, y = 1 = 0.2 if r = 1, y = 1. (1) Please find the marginal distributions of X and Y, respectively ? Fx(x) =? if r = 0, Fx(x) =? if r = 1, Fy(y) =? if y = 0, Fy(y) =? if y = 1. (2) Please find the mean and variance of X. (3) Please find the conditional distribution of X given Y = 1. (3) Please find the conditional distribution of X given Y = 1. Fx|y (x|1) =? if æ = 0, Fx|Y (x|1) =? if a = 1. Note that Fxy(x|y) = P(X = x|Y = y). (4) Please find the conditional expectation of X given Y = 1. E(X|Y = 1) =? (5) Show the relation E[X] = P(X = 1).
11. Let (yı, Y2, .., Yn) be independent random sample from the uniform distribution on [0, 1]. (a) show that Z = – In Y; has exponential distribution with parameter 1. (b) Hence or otherwise, show that –2) In Y; Xản i=1
How to do and I do not know how to do
The joint distribution of X and Y is: Pxy(0,0)=1/25, Pxy(0,1)=a, Pxy(0,2)=2/25 Рxy(1,0)-а, Рx(1,1)-b, Рҳ/(1,2)-а Рxy(2,0)-2/25, Рxx(2,1)-а, Рҳ/(2,2)-1/25 You want "a" to make the variance of Y as minimum as possible. X,Y X,Y 1. Fir The variance of Y equals. Tin Select one: а. 1/2 b. 6/25 с. 2/5 d. 3/5 e. 3/10
(a) Let X1 ~ x² (n, 8) and X2 ~ x² (m, 1). mX1 and its parameters. nX2 (i) Find the distribution of X = (ii) If 1 = 0, name the distribution of X given in 3(a)(i).
Let X₁,..., Xn be an iid random sample from a Uniform(0, 0), where 0 > 0. Let X(n) = max{X₁, (a) Find the mean and variance of X(n). (b) Find the limiting distribution of Zn = n (0 – X (n)). (c) Find the limiting distribution of log(Zn). Xn}
1. Let X1, X,.., X, random sample from distribution be a a Geometric 2....., fx (x) = p(1– p)*| F, (y,) = ? x-1 x=1,2,3,.... Fy, (y,) = ? P(Y, <1) =? а. b. С.
Let Y₁, Y2, Y3, Y₁, Y5 be a random sample of size 5 from a standard normal population. Find the moment generating function of the statistic: X = 2Y₁² + Y₂² + 3Y3²+ Y₂² +4Y5² Let Y₁, Y₂, Y3, Y4, Y5 and X₁, X2,..., X, be independent and normally distributed random samples from populations with means ₁ = 2 and ₂ = 8 and variances ₁² = 5 and ₂² = k₁ respectively. Suppose that P(X-Y> 10) = 0.02275, find the value of 0₂² = k.
11. Let (y1, Y2 ... Yn) be independent random sample from the uniform distribution on [0, 1]. (a) show that Z = – In Y; has exponential distribution with parameter 1. (b) Hence or otherwise, show that -2 In Y; xản
b) Let X₁, X₂,..., X and Y₁, Y₂, ..., Ym be random samples from populations with moment generating 25 functions Mx₁(t) = ³t+t² and My(t) = (₁-¹)²5, respectively. i) Find the sampling distribution of the statistic W = X₁ + 2X₂ − X3 + X4 + X5. ii) What is the value of the sample size n, if P[Σ1(X¡ − X)² > 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|Ỹ - µy| ≥10) < 0.04?
4.
b) Let X₁, X₂, X, and Y₁, Y₂,...,Y be random samples from populations with moment generating 25 functions Mx, (t) = e³t+t² and My(t) = respectively. i) Find the sampling distribution of the statistic W = X₁ + 2X₂-X₂ + X₁ + X5. ii) What is the value of the sample size n, if PIX(X-X)² > 68.3392] = 0.025? iii) What is the value of the sample size m, if P(|-|≥10) < 0.04?

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