B5. Let X₁, X₂, ..., Xn be IID random variable with common expectation µ and common variance o²,and let X = (X₁ + + X₂)/n be the mean of these random variables. We will be considering therandom variable S² given by(a) By writingor otherwise, show thatS²(b) Hence or otherwise, show thatnS² = (x₁ - x)².= Ĺ(X₂i=1X₁ X = (X₁-μ) - (x-μ)= Σ(X; -μ)² - n(X - μ)².i=1ES² = (n-1)0².You may use facts about X from the notes provided you state them clearly. (You may find it helpfulto recognise some expectations as definitional formulas for variances, where appropriate.)(c) At the beginning of this module, we defined the sample variance of the values x₁, x2,...,xn tobeS =1n-1ni=1((x₁ - x)².Explain one reason why we might consider it appropriate to use 1/(n-1) as the factor at thebeginning of this expression, rather than simply 1/n.B6. (New) Roughly how many times should I toss a coin for there to be a 95% chance that between 49%and 510/of my nain toon land Honda?

Let X1, X2, . . . ., Xn be i.i.d. random variable with a common expectation E(Xi)=μ and common…

Answered: B5. Let X₁, X2,..., Xn be IID random…

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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