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Let x1 and x2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. let y1 = (x1/r1)/(x2/r2) and y2 = x2. (a) find the joint pdf of y1 and y2. (b) determine the marginal pdf of y1 and show that y1 has an f distribution. (this is another, but equivalent, way of finding the pdf of f.)
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