If we let X1, X2,...Xn be a random sample from the distribution N( μx = 8, σx = 4), then what would the distribution of (X-8)/(4/√n) be? If we let X1, X2,...X10 be a random sample from the distribution N( μ, σ), then what is the value k so that P( (X-μ)/(σ/√10) < k ) = .05?

If we let X1, X2,...Xn be a random sample from the distribution N( μx = 8, σx = 4), then what would the distribution of (X-8)/(4/√n) be? If we let X1, X2,...X10 be a random sample from the distribution N( μ, σ), then what is the value k so that P( (X-μ)/(σ/√10) < k ) = .05?

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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If we let X₁, X₂,...X_n be a random sample from the distribution N( μ_x = 8, σ_x = 4), then what would the distribution of (X-8)/(4/√n) be?

If we let X₁, X₂,...X₁₀ be a random sample from the distribution N( μ, σ), then what is the value k so that P( (X-μ)/(σ/√10) < k ) = .05?

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B) Let X1,X2, .,Xn be a random sample from a N(u, o2) population with both parameters unknown. Consider the two estimators S2 and ô? for o? where S2 is the sample variance, i.e. s2 =E,(X, – X)² and ở² = 'E".,(X1 – X)². [X = =E-, X, is the sample mean]. %3D n-1 Li%3D1 [Hint: a2 (п-1)52 -~x~-1 which has mean (n-1) and variance 2(n-1)] i) Show that S2 is unbiased for o2. Find variance of S2. ii) Find the bias of 62 and the variance of ô2. iii) Show that Mean Square Error (MSE) of ô2 is smaller than MSE of S?. iv) Show that both S2 and ô? are consistent estimators for o?.