Show that if Y1 has a ? 2 distribution with ?1 degrees of

Chapter 6, Problem 59E

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QUESTION:

Problem 59E

Show that if Y1 has a χ 2 distribution with ν1 degrees of freedom and Y2 has a χ 2 distribution with ν2 degrees of freedom, then U = Y1 + Y2 has a χ 2 distribution with ν1 + ν2 degrees of freedom, provided that Y1 and Y2 are independent.

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QUESTION:

Problem 59E

Show that if Y1 has a χ 2 distribution with ν1 degrees of freedom and Y2 has a χ 2 distribution with ν2 degrees of freedom, then U = Y1 + Y2 has a χ 2 distribution with ν1 + ν2 degrees of freedom, provided that Y1 and Y2 are independent.

ANSWER:

Solution:

Step 1 of 2:

It is given that has distribution with degrees of freedom and  has distribution with degrees of freedom.

A variable U is defined as U=+ .

Now we have to show that U is distributed as   with  + degrees of freedom.


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