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TRUE OR FALSE. a.) Let X (X₁, X2,..., Xn)' be a random vector with joint cumulative distribution function 2 - fx(-). Then (Xi − #i)² has a chi-square distribution with n degrees of freedom where 72 i=1 and o are the mean and variance, respectively, of each of the random variable in X, i = 1,2,..., n. b.) Let X₁, X2,..., Xn be a random sample from a density f(), which has mean and finite n 0² n variance o2, and let X = n X₁. Then E[X] = µ and Var(X) = μ = c.) For any random variables X and Y, E[XY] = E[X] E[Y].

TRUE OR FALSE. a.) Let X (X₁, X2,..., Xn)' be a random vector with joint cumulative distribution function 2 - fx(-). Then (Xi − #i)² has a chi-square distribution with n degrees of freedom where 72 i=1 and o are the mean and variance, respectively, of each of the random variable in X, i = 1,2,..., n. b.) Let X₁, X2,..., Xn be a random sample from a density f(), which has mean and finite n 0² n variance o2, and let X = n X₁. Then E[X] = µ and Var(X) = μ = c.) For any random variables X and Y, E[XY] = E[X] E[Y].

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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TRUE OR FALSE. a.) Let X (X₁, X2,..., Xn)' be a random vector with joint cumulative distribution function 2 - fx(-). Then (Xi − #i)² has a chi-square distribution with n degrees of freedom where 72 i=1 Hand o are the mean and variance, respectively, of each of the random variable in X, i = 1,2,..., n. b.) Let X₁, X2,..., Xn be a random sample from a density f(), which has mean and finite n 0² n variance o2, and let X = n X₁. Then E[X] = µ and Var(X) = μ = c.) For any random variables X and Y, E[XY] = E[X] E[Y].
Transcribed Image Text:TRUE OR FALSE. a.) Let X (X₁, X2,..., Xn)' be a random vector with joint cumulative distribution function 2 - fx(-). Then (Xi − #i)² has a chi-square distribution with n degrees of freedom where 72 i=1 Hand o are the mean and variance, respectively, of each of the random variable in X, i = 1,2,..., n. b.) Let X₁, X2,..., Xn be a random sample from a density f(), which has mean and finite n 0² n variance o2, and let X = n X₁. Then E[X] = µ and Var(X) = μ = c.) For any random variables X and Y, E[XY] = E[X] E[Y].
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