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Show that if Y1 has a ? 2 distribution with ?1 degrees of
Chapter 6, Problem 59E(choose chapter or problem)
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.
Questions & Answers
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.