Show that if y, has a x distribution with v degrees of freedom and Y has...
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Show that if y, has a x² distribution with v₂ degrees of freedom and Y₂ has a ² distribution with v₂ degrees of freedom, then U = Y₁ + Y₂ has a x² distribution with v₁ + v₂ degrees of freedom, provided that Y₁ and Y₂ are independent. The moment-generating function for Y₁ is my, (t) = and the moment-generating function for Y₂ is .Since Y, and Y₂ are independent, the moment-generating function for U is m(t) = which is the moment-generating function for a x2 distribution with v₁ + v₂ degrees of freedom. Show that if y, has a x² distribution with v₂ degrees of freedom and Y₂ has a ² distribution with v₂ degrees of freedom, then U = Y₁ + Y₂ has a x² distribution with v₁ + v₂ degrees of freedom, provided that Y₁ and Y₂ are independent. The moment-generating function for Y₁ is my, (t) = and the moment-generating function for Y₂ is .Since Y, and Y₂ are independent, the moment-generating function for U is m(t) = which is the moment-generating function for a x2 distribution with v₁ + v₂ degrees of freedom.
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Probability and Statistics for Engineers and Scientists
ISBN: 978-0495107576
3rd edition
Authors: Anthony Hayter
Posted Date:
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