Prove Theorem 8.10. Theorem 8.10 If X1 and X2 are independent random variables, X1 has a chi-square

Question:

Prove Theorem 8.10.
Theorem 8.10
If X1 and X2 are independent random variables, X1 has a chi-square with v1 degrees of freedom, and X1 + X2 has a chi-square with v > v1 degrees of freedom, then X2 has a chi-square with v – v1 degrees of freedom.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...