3.6.16. Let X1, X2, and X3 be thrce independent chi-square variables with r1, r2,and ra degrees of freedom, respectively.(a) Show that Y = X1/X2 and Y, = X1 + X2 are independent and that Y, isx*(*1 + r2).%3D(b) Deduce thatX1/rX2/r2X3/r3and(X1 + X2)/(ri + r2)are independent F-variables.

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Answered: 3.6.16. Let X1, X2, and X3 be throe…

MATLAB: An Introduction with Applications

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3.6.16. Let X1, X2, and X3 be throe independent chi-square variables with r1, r2, and ra degrees of freedom, respectively. (a) Show that Yi = X1/X2 and Y2 = X1 + X2 are independent and that Y, is x*(rı + ra). %3D (b) Deduce that X1/r X2/r2 X3/r3 and (X1 + X2)/(r + ra) are independent F-variables.