Prove Theorem 8.9. Theorem 8.9 If X1, X2, . . . , Xn are independent random variables

Question:

Prove Theorem 8.9.
Theorem 8.9
If X1, X2, . . . , Xn are independent random variables having chi- square distributions with v1, v2, . . . , vn degrees of freedom, then

Has the chi-square distribution with v1 + v2 + · · · + vn 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...