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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Author:Amos Gilat

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Q2.1 have been given the following sets functions. Which of are linearly you them on the interval of (-∞0, ∞0) ? one right answer. more than independent There may be Leption f₁ (x) = x²₂ f₁₂ (x) = 3x²₂ f₂(x) = x² +6 option 2 f₁cx) = 3e³x₂f₂(x) = 9e⁹x - f₁₂(x) = 276²7x option 3 2 f₁(x) = 2sin ²³ x ₂ f₂(x) = 6 cos ²³ x 9 f₂(x)=x of
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2. Assuming the dichotomous disease model, with Y1 and Y2 being two relatives with relatedness R, show that (a) Cov(Y1, Y2) = P(Y1 = Y2 = 1) – K². (b) express R as a function of the covariance and K.

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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.