If X1, X2, and X3 are uncorrelated variables each having the same standard deviation, show that the coefficient of correlation between X1 X2 and X2 X3 is equal to (1)/(2). Why is the correlation coefficient not zero? | Numerade
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Suppose X, Y and Z are uncorrelated random variables with means1, 2 and 3 and standard deviations 2, 4 and 5 respectively. If U =Y – X and V = Z – Y. Compute the correlation coefficient between Uand V and comment on your result
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Suppose that the idiosyncratic errors in (14.4),{ui t: t=1,2, …, T}, are serially uncorrelated with constant variance, σu^2 . Show that the correlation between adjacent differences, Δui t and Δui, t+1, is -.5. Therefore, under the ideal FE assumptions, first differencing induces negative serial correlation of a known value. | Numerade
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