Suppose that X,...,X are i.i.d. random variables and let X = 1/1 X. (a) Show that...

    

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Suppose that X,...,X are i.i.d. random variables and let X = 1/1 X. (a) Show that the sum of residuals always equal to zero, i.e., show that (b) Show that n (x; x) = 0. i=1 n (x x) = (x?) - n(X). i=1 i=1 (c) Please answer the following questions and provide a brief explanation to your answers. - What is the degree of freedom of (X,...,xn)? What is the degree of freedom of (X,..., X, X)? What is the degree of freedom of the residuals: (X-X,..., Xn-X)? - - What is the degree of freedom of (X X, Xn - X,X) ? Suppose that X,...,X are i.i.d. random variables and let X = 1/1 X. (a) Show that the sum of residuals always equal to zero, i.e., show that (b) Show that n (x; x) = 0. i=1 n (x x) = (x?) - n(X). i=1 i=1 (c) Please answer the following questions and provide a brief explanation to your answers. - What is the degree of freedom of (X,...,xn)? What is the degree of freedom of (X,..., X, X)? What is the degree of freedom of the residuals: (X-X,..., Xn-X)? - - What is the degree of freedom of (X X, Xn - X,X) ?