b)X-XN (0,1), and W₁σχYHYN(0,1), for i=1,2,3,...,10, then:Let Z₁ =i) State, with parameter(s), the probability distribution of the statistic, T =ay10ΣW2√Σt,w₁²ii) Find the mean and variance of the statistic T =10Σ{12/2iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4.iv) Find the value of ß such that P(T> B) = 0.01, where T = E₁Z²+₁ W².

Given Zi~N(0,1) and Wi~N(0,1) Result: t~F(a,b) Then Mean=E(t)=b/(b-2) V(t)=2b2 (a+b-2)/[a(b-2)2…

Answered: b) Let Z₁ = X-x~N (0,1), and Wi σχ…

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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K 2) d) Find the value of t and p if P(t t) : = 3) Suppose that X~x²(v) and Y~x²(n). If µx = 6, o²y = 16 and W a) State with parameter(s) the distribution of W. 4X 3Y Ơ V = then
a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) you and Y = -√n. VR i) Show that the standard score of the sample mean X, is equal to Y. ii) Show that the mean and variance of the random variable Y are 0 and 1, respectively. iii) Show using the moment generating function technique that Y is a standard normal rando... variable. iv) What is the probability that Y² is between 0.02 and 5.02? b) Let X₁, X₂, X, and Y₁, Y₂.... Y be random samples from populations with moment generating functions Mx, (t) = eat+t² and My (t) = (-), respectively. 25 i) Find the sampling distribution of the statistic W = X₁ + 2X₂ X3 + 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(|Y-Hy ≥10) <0.04? QUESTION A
2) Consider a standard normal random variable X and Y-Exp(ß = 1). If W = 2Y and Z = VIX, then a) State with parameter(s) the probability distribution of Z. b) Find the mean and variance of Z. c) d) Find the value of T if P(Z > T): 1000 Compute the probability that Z is at most 6.97.
A box has 3white(W) balls,2 black (B) balls and 4 red(R) balls. Two balls were drawn successively from this box (i) with replacement/ (ii) without replacement. Let X=the number of white balls drawn and let Y=the number of black balls drawn.
Let (Ω, Pr) be a probability space, and let X and Y be two independent random variables that are positive and have non-zero variance. (a) Prove that X^2 and Y are independent. Note that by symmetry, it will also follow that Y^2 and X are independent. (b) Use the result from part (a) to show that the random variables W = X + Y and Z = XY are positively correlated (i.e. Cov(W, Z) > 0).
Is the following statements correct or incorrect: Suppose that a random vector Y' = (Y1, Y2, Y3) has multi-normal distribution with mean vector u and variance-covariance matrix £ given by and Σ 흑 0 1 respectively. CH), Then the distribution of Z = Y is N 1
Q6. In the following diagram: Họ: µ = 4 ; H1: µ= 1. f(X) Ho Xp Rejection region Non-rejection region Examine the probabilities represented by the regions, a,b and c. Identify the incorrect statement: A. a = Pr(Type I error 'AND’ Not-Type II error). B. a +b = Pr(Type I error). С.с 3D Pr(Туpe Il error). D. a + b + c = Pr(Type I error 'OR’ Type II error) %3D A. A В. В С. С O D. D
c) Suppose that a random variable Y is uniformly distributed on an interval (0,1) and let c> 0 be a constant. i) Find the moment generating function of X = -cY. ii) What is the distribution of X? 2| Page
Let S. be the time it takes a standard Brownian motion to hit a. Find the probabilities 1) P(S2 < S_4), 1) P(S < S_2 < S4), 2) P(S1 < S_2 < S1 < S12).
3 Let X be a random variable with probability Law P (X = r) = q, K for r = 1,2,3.. . 00, Find the moment generating function and mean of ihe random variable X. Let K+ q = 1.
Let Z₁ = X₁-μx ~N(0,1), and Wi σχ = Yi-HY~N(0,1), for i = 1,2,3,...,10, then: oy i) State, with parameter(s), the probability distribution of the statistic, T = ii) Find the mean and variance of the statistic T = Σt, wi? Σ, Z² Σt=1Zi 4i=1 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of such that P(T > B) = 0.01, where T = Σ₁₁Z₁² + 10₁ W₁². ẞ Σ{1Z2 Σi,

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