Recall the simple regression modelY = a + 3X + €where the random error & ~ N(0,02). Let 3 be the MLE estimator of the slope ß. InHomework 3 Exercise 3, we found the distribution of this point estimator to beجور عليهB~N0²nVxwhere v is the variance of the empirical distribution of x1, x2,, Xn. (i) Verify thatP(|3 – ß| ≤ €) = 1 - aand conclude that, if σ is known,Xi:Yi:Xi:Yi:O/nVTis a 100(1 a)% confidence interval of B.(ii) Suppose we know that σ = 2 and are given the following data points (x₁, yi):oZa/212Give a 95% confidence interval of 3¹.E =B + Za/27OZa/21 /nvxO/nv x4.44 5.18 -3.08 3.99 4.39 3.3 -1.25 1.0314.1116.61 -0.58 15.78 13.2 12.692.93 5.274.091.514.254.33 -2.75 -2.85 -2.57 3.1615.56 -2.43 -4.66 0.59 11.6713.816.07 14.78

Given that β^~Nβ, σ2nvx, where vx is the variance of the empirical distribution of x1, x2,..., xn.…

Answered: (i) Verify that P(|38| ≤e) = 1-a and…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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