(a) Let X1, X2, X3, X4 be a sample from U(0, 1), and let X(1),X(2), X(3), X(4) be the cor -responding order statistics. Find the probability density function for each of the randomvariables: i. X(2) [1] ii. X(3) – X(1) [1] iii. X(4) – X(2) [1] iv. 1 – X(3)

The random sample from the distribution is .The corresponding order statistics are .The probability…

Answered: (a) Let X1, X2, X3, X4 be a sample from…

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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Consider the following simple linear regression. iid Y = Po + B₁X + e, e~ N(0,02), i=1,..., n.
O Prove that E(X) = E(X/Y), where X and Y are two random variables which are independent. %D
Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0
Can you help me please:
(b) Let X₁, X₂, X3 be uncorrelated random variables, having the same variance ². Consider the linear transformations Y₁ = X₁ + X₂, Y₂ = X₁ + X3 and Y3 = X₂ + X3 . Find the correlations of Yi, Y; for i #j. (5 marks)
A- Let x be a discrete random variable with probability distribution function f(x)=k( x2 +20) and x= −1,1,2,3. Find the value of k. Find the Variance of X. B- Let x denote a discrete random variable which can take the values −2,0, and 5. Given that the expectation of X is 8/100 and P(X=−2)=8/20 , find P(X=5).
Answers for a, b and c
Consider a random sample from the distribution of Binomial, Poisson, Exponential, Gamma, and normal. Let T1 = X + 4 ; T2 = (X – 1); T3 = X1+4X2 – 3X3 & T4 = E7 X; /(n + 1). Find the MSE of each statistics and choose the best statistic.
Let X be a random variable with pmf P(O)=0.2, P(1)-0.5, P(2)=0.3. Let F(X) be the cdf of X. (a) Find P(X<0.7) (b) Find F(1.3). (c) Find F(3).
Let X be the random variable with PMF: p(x) = k(]x – 2|+ 1), for x= -2, -1, 0, 1, 2 0, elsewhere (a) Find the value of k (b)Find the PMF of X (c) Find the mean, variance, and the standard deviation of X
Assume that McDonalds can serve a customer's order in X minutes after the customer enters the fast food chain. The PDF of the random variable X is shown as: 0.1 10 Moreover, assume that the customer can finish the food Y minutes after it is served, independent of the serving time. The PDF of the random variable Y is shown as: i. ii. |fx(x) 0.1 fy(y) fy(y) = 0.1e-0.1y 50 Let Z = X + Y be the total amount of time that the customer stays inside the fast food chain. 15 20 What is the probability that the customer stays within McDonalds for at most 18 minutes, i.e. P(Z < 18)? What is the expected value (in minutes) that the customer stays within the fast food chain?

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(a) Let X1, X2, X3, X4 be a sample from U(0, 1), and let X(1), X(2), X(3), X(4) be the cor - responding order statistics. Find the probability density function for each of the random variables: i. X(2) [1] ii. X(3) – X(1) [1] iii. X(4) — X(2) [1] iv. 1 – X(3)