B2. Consider the random variables X and Y; from question B1 again.(a) Show that the sample covariance is an unbiased estimator of Cov(X₁,Y₁).Hint: consider the equality X; X = (X₂ − µ) – (X -μ).(b) Can you conclude from the statement in part (a) that the sample correlation is anunbiased estimator of Corr(X₁, Y₁)? Justify your answer.

Step 1: proove part (a)a)Recall that the sample covariance between X and Y is defined as:Cov(X,Y) =…

Answered: le covariance is an unbiased estimator…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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- (Sec. 6.1) Using a long rod that has length µ (unknown), you are going to lay out a square plot in which the length of each side is µ. Thus the area of the plot will be µ². However, because you do not know the value of µ, you decide to make n independent measurements X1,...,X, of the length. Assume that each X; has mean µ and variance o². (a) Show that X² is not an unbiased estimator for the area of the square plot µ². [Hint: for any rv Y, E[Y²] = V[Y] + E[Y]². Apply this for Y = X.] (b) For what value of k is the estimator X² – kS² unbiased for µ²?
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le covariance is an unbiased estimator of Cov(X₁, Y₁). equality X₁ X = (Xi − µ) — (X − µμ). - - - om the statement in part (a) that the sample correlation is an of Corr(X1₁, Y₁)? Justify your answer.